In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects： {ψt=-（1-α）...In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects： {ψt=-（1-α）ψ-θx＋αψxx, θt=-（1-α）θ＋νψx＋（ψθ）x＋αθxx（E） with initial data （ψ,θ）（x,0）=（ψ0（x）,θ0（x））→（ψ±,θ±）as x→±∞ where α and ν are positive constants such that α 〈 1, ν 〈 4α（1 - α）. Under the assumption that ｜ψ＋ - ψ-｜ ＋ ｜θ＋ - θ-｜ is sufficiently small, we show the global existence of the solutions to Cauchy problem （E） and （I） if the initial data is a small perturbation. And the decay rates of the solutions with exponential rates also are obtained. The analysis is based on the energy method.展开更多
It is known that the one-dimensional nonlinear heat equation ut ： f（u）x1x1, f＇（u） 〉 0, u（±∞, t） ： u, u＋ ≠ u- has a unique self-similar solution u（x1/√1＋t）. In multi-dimensional space, （x1/√1＋t...It is known that the one-dimensional nonlinear heat equation ut ： f（u）x1x1, f＇（u） 〉 0, u（±∞, t） ： u, u＋ ≠ u- has a unique self-similar solution u（x1/√1＋t）. In multi-dimensional space, （x1/√1＋t） is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation： ut -△f（u） = 0, x ∈ R^n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping： utt ＋ ut - △f（u） = 0, x ∈ R^n. The time decay rate is also obtained. The proofs are given by an elementary energy method.展开更多
In this paper, we will show that under some smallness conditions, the planar diffusion wave v（x1/√＋t）is stable for a quasilinear wave equation with nonlinear damping：vtt-△f（v）＋vt＋g（vt）=0_3 x=（x1,x2…,xn）...In this paper, we will show that under some smallness conditions, the planar diffusion wave v（x1/√＋t）is stable for a quasilinear wave equation with nonlinear damping：vtt-△f（v）＋vt＋g（vt）=0_3 x=（x1,x2…,xn）∈Rn,where v（x1/√1＋t）is the unique similar solution to the one dimensional nonlinear heat equa-tion：vt-f（v）x1 x1=0,f＇（v）〉0,v＋（∞,t）=v±,v＋≠v_.We also obtain the L∞ time decay rate whichreads‖v-v‖L∞=О（1）（1＋t）-r/4,where r=min（3,n）.To get the main result, the energy method and a newinequality have been used.展开更多
This study presents the diffusive wave model,relevant dispersion law and the applications to the signal transduction of live cells,phason dynamics of quasicrystals,Brownian movement,electro-magnetic field and fluid dy...This study presents the diffusive wave model,relevant dispersion law and the applications to the signal transduction of live cells,phason dynamics of quasicrystals,Brownian movement,electro-magnetic field and fluid dynamics fluctuation,respectively.The common features of these diffusive waves are summarized,which present diffusion as well as wave behaviour,or exactly speaking,they present a duality of diffusion and wave or the duality of wave and diffusion.Furthermore,the general nature of the motion is discussed from the point of view of Landau elementary excitation of condensed matter,this may lead to a concept of generalized elementary excitation（or generalized quasiparticle） corresponding to the diffusive wave.展开更多
A combination of the rainfall-runoff module of the Xin’anjiang model, the Muskingum routing method, the water stage simulating hydrologic method, the diffusion wave nonlinear water stage method, and the real-time err...A combination of the rainfall-runoff module of the Xin’anjiang model, the Muskingum routing method, the water stage simulating hydrologic method, the diffusion wave nonlinear water stage method, and the real-time error correction method is applied to the real-time flood forecasting and regulation of the Huai River with flood diversion and retarding areas. The Xin’anjiang model is used to forecast the flood discharge hydrograph of the upstream and tributary. The flood routing of the main channel and flood diversion areas is based on the Muskingum method. The water stage of the downstream boundary condition is calculated with the water stage simulating hydrologic method and the water stages of each cross section are calculated from downstream to upstream with the diffusion wave nonlinear water stage method. The input flood discharge hydrograph from the main channel to the flood diversion area is estimated with the fixed split ratio of the main channel discharge. The flood flow inside the flood retarding area is calculated as a reservoir with the water balance method. The faded-memory forgetting factor least square of error series is used as the real-time error correction method for forecasting discharge and water stage. As an example, the combined models were applied to flood forecasting and regulation of the upper reaches of the Huai River above Lutaizi during the 2007 flood season. The forecast achieves a high accuracy and the results show that the combined models provide a scientific way of flood forecasting and regulation for a complex watershed with flood diversion and retarding areas.展开更多
In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this...In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this kind of model in one dimensional case for general perturbations by constructing some correction functions to delete the gaps between the original solutions and the diffusion waves in L2-space, and by using a key inequality we prove the stability of diffusion waves. As the same time, the convergence rates are also obtained.展开更多
A diffuse acoustic field has been increasingly used to infer temporal changes in the structures,such as early dislo-cations and microcracking.This study explores three different techniques to characterise acoustic fie...A diffuse acoustic field has been increasingly used to infer temporal changes in the structures,such as early dislo-cations and microcracking.This study explores three different techniques to characterise acoustic field by using a single ultrasonic phased array.The first two techniques are proposed to measure spatial uniformity of wave field by examining differences in the integral of energy and the maximum energy respectively at multiple inspection loca-tions.The third one is developed to evaluate the degree of phase coherence between propagating waves transmitted sequentially by two neighbouring array elements.The efficacy of these techniques are investigated by examining their metrics on simulations and well-known samples.The results suggest that two selected metrics can be used to quantitatively estimate the diffuse field start time as well as the field size by comparing their value with the idealised diffuse state(15%for the energy integral metric,ηarea and 1 for the phase coherence metric,ηphase)and identifying the convergence start point.展开更多
In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the ...In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the global existence of strong solutions for the initial boundary value problem in the quarter plane. In particular, we show that in large time, these solutions tend to the nonlinear diffusion wave which is different from the steady state, at an algebraic time-decay rate. As far as we know, this is the first result about the nonlinear diffusion wave phenomena of the solutions for the one-dimensional drift-diffusion model in the quarter plane.展开更多
Pollutant transport in overland flow over surfaces with spatially varying microtopography,roughness,and infiltration was investigated using the diffusion wave equation and transport rate-based equation.The finite volu...Pollutant transport in overland flow over surfaces with spatially varying microtopography,roughness,and infiltration was investigated using the diffusion wave equation and transport rate-based equation.The finite volume method in space and an implicit backward difference scheme in time were employed in the numerical solution of the 2D governing equations.The developed model was first tested against an analytical solution and an experimental study involving overland flow and the associated pollutant transport,subsequently a series of numerical tests were carried out.Non-point source pollution was investigated under spatially varying microtopography,roughness,and infiltration.The simulation results showed that microtopography and roughness were the dominant factors causing significant spatial variations in solute concentration.When the spatially varying microtopography was replaced by a smooth surface,the result was an overestimation of the solute rate at the outlet of the upland.On the other hand,when the spatially varying roughness was replaced by the average roughness and spatially varying infiltration rate by the average infiltration rate,the pollutant discharge at the outlet of the upland was not significantly affected.The numerical results further showed that one cannot ignore the spatial variations of slope and roughness when investigating the local pollutant concentration distribution.展开更多
The rheological properties of two specific waterborne polyurethane （PU） paints were studied by both macrorheological and microrheological methods. During the macrorheological measurement on a rotary rheometer, evapo...The rheological properties of two specific waterborne polyurethane （PU） paints were studied by both macrorheological and microrheological methods. During the macrorheological measurement on a rotary rheometer, evaporation of solvent cannot be totally excluded, which has an influence on the reliability of rheological results. So, the linear oscillatory frequency sweep results （storage and loss modulus versus frequency） and steady shear results （viscosity versus shear rate） got from the rotary rheometer measurement are only used for qualitative analysis. As the evaporation of solvent can be neglected during microrheological measurements on a diffusing wave spectroscope （DWS）, the results of storage modulus （G3 and loss modulus （G＇~） versus frequency are more credible than the results obtained from the rotary rheometer measurement. Thus, the results of G＇ and G＂ versus frequency from DWS measurements are used for quantitative analysis in this work. The G＇ for both of the waterborne PU paints are larger than G＂ at low frequency and that is opposite at high frequency in the experimental angular frequency range. The values of modulus at same frequency and viscosity at low shear rate for the two PU paints have apparent difference, which determines the difference of their application.展开更多
The aim of this work is to provide a formulation of two related nonlinear diffusive convective models in the form of coupled reaction-absorption equations.First,the postulated models are studied with an analytical app...The aim of this work is to provide a formulation of two related nonlinear diffusive convective models in the form of coupled reaction-absorption equations.First,the postulated models are studied with an analytical approach.Later on,numerical evidences are considered to account for a precise characterization.The problem(P)analyzed is of the form:ut=δΔu+c⋅∇u+v^(n),vt=ϵΔv+c⋅∇v−um,n,m∈(0,1),u_(0)(x),v_(0)(x)>0∈L^(1)_(loc)(RN)∩L^(∞)(R^(N)).(0.1)Afterwards,a related problem P_(T)is studied:ut=δΔu+c⋅∇u−v^(n)(u−d),vt=ϵΔv+c⋅∇v−u^(m)v,n,m∈(0,1),u_(0)(x),v_(0)(x)>0∈L^(1)_(loc)(R^(N))∩L^(∞)(R^(N)).(0.2)The principal aspects for analysis are related to the existence and the derivation of particular solutions to reproduce the dynamic of the interacting species.For the problem PT,we make use of the TW approach to study existence of solutions and precise evolution of profiles.Note that the term predator is used to refer to an invasive behavior,while the term prey is used for the invaded species.展开更多
基金The research is supported by Program for New Century Excellent Talents in University #NCET-04-0745the Key Project of the National Natural Science Foundation of China #10431060the Key Project of Chinese Ministry of Education #104128
文摘In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects： {ψt=-（1-α）ψ-θx＋αψxx, θt=-（1-α）θ＋νψx＋（ψθ）x＋αθxx（E） with initial data （ψ,θ）（x,0）=（ψ0（x）,θ0（x））→（ψ±,θ±）as x→±∞ where α and ν are positive constants such that α 〈 1, ν 〈 4α（1 - α）. Under the assumption that ｜ψ＋ - ψ-｜ ＋ ｜θ＋ - θ-｜ is sufficiently small, we show the global existence of the solutions to Cauchy problem （E） and （I） if the initial data is a small perturbation. And the decay rates of the solutions with exponential rates also are obtained. The analysis is based on the energy method.
基金Acknowledgements He＇s research is supported in part by National Basic Research Program of China （Grant No. 2006CB805902）. Huang＇ research is supported in part by National Natural Science Foundation of China for Distinguished Youth Scholar （Grant No. 10825102）, NSFC-NSAF （Grant No. 10676037） and National Basic Research Program of China （Grant No. 2006CB805902）.
文摘It is known that the one-dimensional nonlinear heat equation ut ： f（u）x1x1, f＇（u） 〉 0, u（±∞, t） ： u, u＋ ≠ u- has a unique self-similar solution u（x1/√1＋t）. In multi-dimensional space, （x1/√1＋t） is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation： ut -△f（u） = 0, x ∈ R^n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping： utt ＋ ut - △f（u） = 0, x ∈ R^n. The time decay rate is also obtained. The proofs are given by an elementary energy method.
基金Supported by the National Natural Science Foundation of China(No.11201301)Shanghai University Young Teacher Training Program(No.slg12026)
文摘In this paper, we will show that under some smallness conditions, the planar diffusion wave v（x1/√＋t）is stable for a quasilinear wave equation with nonlinear damping：vtt-△f（v）＋vt＋g（vt）=0_3 x=（x1,x2…,xn）∈Rn,where v（x1/√1＋t）is the unique similar solution to the one dimensional nonlinear heat equa-tion：vt-f（v）x1 x1=0,f＇（v）〉0,v＋（∞,t）=v±,v＋≠v_.We also obtain the L∞ time decay rate whichreads‖v-v‖L∞=О（1）（1＋t）-r/4,where r=min（3,n）.To get the main result, the energy method and a newinequality have been used.
基金Sponsored by the National Natural Science Foundation of China(10672022)
文摘This study presents the diffusive wave model,relevant dispersion law and the applications to the signal transduction of live cells,phason dynamics of quasicrystals,Brownian movement,electro-magnetic field and fluid dynamics fluctuation,respectively.The common features of these diffusive waves are summarized,which present diffusion as well as wave behaviour,or exactly speaking,they present a duality of diffusion and wave or the duality of wave and diffusion.Furthermore,the general nature of the motion is discussed from the point of view of Landau elementary excitation of condensed matter,this may lead to a concept of generalized elementary excitation（or generalized quasiparticle） corresponding to the diffusive wave.
基金supported by the National Natural Science Foundation of China (Grant No 50479017)the Program for Changjiang Scholars and Innovative Research Teams in Universities (Grant No IRT071)
文摘A combination of the rainfall-runoff module of the Xin’anjiang model, the Muskingum routing method, the water stage simulating hydrologic method, the diffusion wave nonlinear water stage method, and the real-time error correction method is applied to the real-time flood forecasting and regulation of the Huai River with flood diversion and retarding areas. The Xin’anjiang model is used to forecast the flood discharge hydrograph of the upstream and tributary. The flood routing of the main channel and flood diversion areas is based on the Muskingum method. The water stage of the downstream boundary condition is calculated with the water stage simulating hydrologic method and the water stages of each cross section are calculated from downstream to upstream with the diffusion wave nonlinear water stage method. The input flood discharge hydrograph from the main channel to the flood diversion area is estimated with the fixed split ratio of the main channel discharge. The flood flow inside the flood retarding area is calculated as a reservoir with the water balance method. The faded-memory forgetting factor least square of error series is used as the real-time error correction method for forecasting discharge and water stage. As an example, the combined models were applied to flood forecasting and regulation of the upper reaches of the Huai River above Lutaizi during the 2007 flood season. The forecast achieves a high accuracy and the results show that the combined models provide a scientific way of flood forecasting and regulation for a complex watershed with flood diversion and retarding areas.
基金X.Li’s research was supported in part by NSFC(11301344)Y.Yong’sresearch was supported in part by NSFC(11201301)
文摘In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this kind of model in one dimensional case for general perturbations by constructing some correction functions to delete the gaps between the original solutions and the diffusion waves in L2-space, and by using a key inequality we prove the stability of diffusion waves. As the same time, the convergence rates are also obtained.
基金Supported by Anhui Provincial Natural Science Foundation of China(Grant No.2008085J24)Anhui Provincial Science and Technology Major Project of China(Grant No.201903a05020010)+2 种基金Young Talent Support Program of China Association for Science and Technology(Grant No.[2020]No.87)Doctoral Science and Technology Foundation of Hefei General Machinery Research Institute(Grant No.2019010381)Anhui Provincial Key Research and Development Plan of China(Grant No.202004a05020003).
文摘A diffuse acoustic field has been increasingly used to infer temporal changes in the structures,such as early dislo-cations and microcracking.This study explores three different techniques to characterise acoustic field by using a single ultrasonic phased array.The first two techniques are proposed to measure spatial uniformity of wave field by examining differences in the integral of energy and the maximum energy respectively at multiple inspection loca-tions.The third one is developed to evaluate the degree of phase coherence between propagating waves transmitted sequentially by two neighbouring array elements.The efficacy of these techniques are investigated by examining their metrics on simulations and well-known samples.The results suggest that two selected metrics can be used to quantitatively estimate the diffuse field start time as well as the field size by comparing their value with the idealised diffuse state(15%for the energy integral metric,ηarea and 1 for the phase coherence metric,ηphase)and identifying the convergence start point.
基金Supported by the National Natural Science Foundation of China(11171223)
文摘In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the global existence of strong solutions for the initial boundary value problem in the quarter plane. In particular, we show that in large time, these solutions tend to the nonlinear diffusion wave which is different from the steady state, at an algebraic time-decay rate. As far as we know, this is the first result about the nonlinear diffusion wave phenomena of the solutions for the one-dimensional drift-diffusion model in the quarter plane.
基金Project supported by the National Natural Science Foundation of China (No. 51009120)the Research Fund for the Doctoral Program of Higher Education of China (No. 20090101120065)the State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau of China (No. 10501-243)
文摘Pollutant transport in overland flow over surfaces with spatially varying microtopography,roughness,and infiltration was investigated using the diffusion wave equation and transport rate-based equation.The finite volume method in space and an implicit backward difference scheme in time were employed in the numerical solution of the 2D governing equations.The developed model was first tested against an analytical solution and an experimental study involving overland flow and the associated pollutant transport,subsequently a series of numerical tests were carried out.Non-point source pollution was investigated under spatially varying microtopography,roughness,and infiltration.The simulation results showed that microtopography and roughness were the dominant factors causing significant spatial variations in solute concentration.When the spatially varying microtopography was replaced by a smooth surface,the result was an overestimation of the solute rate at the outlet of the upland.On the other hand,when the spatially varying roughness was replaced by the average roughness and spatially varying infiltration rate by the average infiltration rate,the pollutant discharge at the outlet of the upland was not significantly affected.The numerical results further showed that one cannot ignore the spatial variations of slope and roughness when investigating the local pollutant concentration distribution.
基金financially supported by the National Natural Science Foundation of China(Nos.2127415251473168 an21234007)
文摘The rheological properties of two specific waterborne polyurethane （PU） paints were studied by both macrorheological and microrheological methods. During the macrorheological measurement on a rotary rheometer, evaporation of solvent cannot be totally excluded, which has an influence on the reliability of rheological results. So, the linear oscillatory frequency sweep results （storage and loss modulus versus frequency） and steady shear results （viscosity versus shear rate） got from the rotary rheometer measurement are only used for qualitative analysis. As the evaporation of solvent can be neglected during microrheological measurements on a diffusing wave spectroscope （DWS）, the results of storage modulus （G3 and loss modulus （G＇~） versus frequency are more credible than the results obtained from the rotary rheometer measurement. Thus, the results of G＇ and G＂ versus frequency from DWS measurements are used for quantitative analysis in this work. The G＇ for both of the waterborne PU paints are larger than G＂ at low frequency and that is opposite at high frequency in the experimental angular frequency range. The values of modulus at same frequency and viscosity at low shear rate for the two PU paints have apparent difference, which determines the difference of their application.
文摘The aim of this work is to provide a formulation of two related nonlinear diffusive convective models in the form of coupled reaction-absorption equations.First,the postulated models are studied with an analytical approach.Later on,numerical evidences are considered to account for a precise characterization.The problem(P)analyzed is of the form:ut=δΔu+c⋅∇u+v^(n),vt=ϵΔv+c⋅∇v−um,n,m∈(0,1),u_(0)(x),v_(0)(x)>0∈L^(1)_(loc)(RN)∩L^(∞)(R^(N)).(0.1)Afterwards,a related problem P_(T)is studied:ut=δΔu+c⋅∇u−v^(n)(u−d),vt=ϵΔv+c⋅∇v−u^(m)v,n,m∈(0,1),u_(0)(x),v_(0)(x)>0∈L^(1)_(loc)(R^(N))∩L^(∞)(R^(N)).(0.2)The principal aspects for analysis are related to the existence and the derivation of particular solutions to reproduce the dynamic of the interacting species.For the problem PT,we make use of the TW approach to study existence of solutions and precise evolution of profiles.Note that the term predator is used to refer to an invasive behavior,while the term prey is used for the invaded species.
