In this article, the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered. Using the methods of boundary function and fractional steps, we construct the formu...In this article, the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered. Using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and point out that the boundary layer at t = 0 has a great influence upon the interior layer at t = a. At the same time, on the basis of differential inequality techniques, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of our result. The result of this article is new and it complements the previously known ones.展开更多
In this article, we study a kind of vector singularly perturbed delay-amerenum equation. Using boundary layer function method and geometric analysis skill, the asymptotic expression of the system is constructed and th...In this article, we study a kind of vector singularly perturbed delay-amerenum equation. Using boundary layer function method and geometric analysis skill, the asymptotic expression of the system is constructed and the uniform validity of asymptotic solution is also proved.展开更多
In this paper, a class of strongly nonlinear singularly perturbed interior layer problems are considered by the theory of differential inequalities and the corrective theory of interior layer. The existence of solutio...In this paper, a class of strongly nonlinear singularly perturbed interior layer problems are considered by the theory of differential inequalities and the corrective theory of interior layer. The existence of solution is proved and the asymptotic behavior of solution for the boundary value problems are studied. And the satisfying result is obtained.展开更多
An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior laye...An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior layer solution to the initial boundary value problem are studied.展开更多
In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids....In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.展开更多
A recent study by Liu et al.(2020)suggested that due to the saturation of equatorially trapped planetary waves with different dynamical types,temporal periods,meridional and baroclinic modes,complex layer structures o...A recent study by Liu et al.(2020)suggested that due to the saturation of equatorially trapped planetary waves with different dynamical types,temporal periods,meridional and baroclinic modes,complex layer structures of vertical velocity shear and hence turbulent mixing could frequently occur in the thermocline of the eastern equatorial Pacific.We investigated the occurrence of the interior turbulent mixing as indicated by shear instabilities,above the Equatorial Undercurrent(EUC)core at three equatorial sites along 140°W,170°W,and 165°E,respectively,based mainly on data from the Tropical Atmosphere and Ocean(TAO)mooring array.We found that turbulent mixing bursts persisted in the thermocline of all three sites.Specifically,the interior turbulent mixing layers(ITMLs)could occur in probability of approximately 68%,53%,and 48%at the three sites,respectively.The overall occurrence probability shows obvious and similar biannual variations at 140°W and 170°W,which is higher in boreal from late summer to winter and lower in spring.Vertically,the ITMLs are primarily located above the EUC core and prevail in deeper(shallower)layers from late summer to winter(spring).Most ITMLs(70%)lasted for hours to 3 days,and a few of them(15%)for more than 7 days.The thicknesses of ITMLs were concentrated between 15 and 55 m.At 165°E,the vertical distribution of ITML occurrence probability was different from that at 140°W and 170°W,as it did not show a preference for depths;the durations of ITMLs are short(also from hours to several days)and their thicknesses were between 5 and 25 m.These properties,particularly the high occurrence probability,and short durations demonstrated the persistence of thermocline mixing in the western to eastern equatorial Pacific thermocline and confirmed the generation mechanism by persistent equatorial waves as well.展开更多
The shift of shock position for a class of nonlinear singularly perturbed problems is considered using a special and simple method. The location of the shock wave will be larger moved, even from interior layer to the ...The shift of shock position for a class of nonlinear singularly perturbed problems is considered using a special and simple method. The location of the shock wave will be larger moved, even from interior layer to the boundary layer when the boundary conditions change smaller.展开更多
基金Supported by the National Natural Science Funds (11071075)the Natural Science Foundation of Shanghai(10ZR1409200)+1 种基金the National Laboratory of Biomacromolecules,Institute of Biophysics,Chinese Academy of Sciencesthe E-Institutes of Shanghai Municipal Education Commissions(E03004)
文摘In this article, the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered. Using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and point out that the boundary layer at t = 0 has a great influence upon the interior layer at t = a. At the same time, on the basis of differential inequality techniques, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of our result. The result of this article is new and it complements the previously known ones.
基金supported by the National Science Foundation of China(11071075)Introducing Talents Program of SIT (YJ2013-33)
文摘In this article, we study a kind of vector singularly perturbed delay-amerenum equation. Using boundary layer function method and geometric analysis skill, the asymptotic expression of the system is constructed and the uniform validity of asymptotic solution is also proved.
基金Supported by the National Natural Science Foundation of China(No.10071048)the Zhejiang Education Office(No.20030594)Huzhou Teachers College(No.200302).
文摘In this paper, a class of strongly nonlinear singularly perturbed interior layer problems are considered by the theory of differential inequalities and the corrective theory of interior layer. The existence of solution is proved and the asymptotic behavior of solution for the boundary value problems are studied. And the satisfying result is obtained.
基金supported by the National Natural Science Foundation of China(40876010)the "Strategic Priority Research Program-Climate Change:Carbon Budget and Relevant Issues" of the Chinese Academy of Sciences (XDA01020304)+3 种基金the Natural Science Foundation of Jiangsu Province (BK2011042)the Natural Science Foundation of Zhejiang Province (Y6110502)the Foundation of the Education Department of Fujian Province (JA10288)the Natural Science Foundation from the Education Bureau of Anhui Province (KJ2011A135)
文摘An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior layer solution to the initial boundary value problem are studied.
文摘In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.
基金Supported by the National Natural Science Foundation of China(NSFC)(No.41730534)the Laoshan Laboratory Science and Technology Innovation Program(No.LSKJ 202202502)+1 种基金the NSFC(Nos.41976012,42090044)the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDB42000000)。
文摘A recent study by Liu et al.(2020)suggested that due to the saturation of equatorially trapped planetary waves with different dynamical types,temporal periods,meridional and baroclinic modes,complex layer structures of vertical velocity shear and hence turbulent mixing could frequently occur in the thermocline of the eastern equatorial Pacific.We investigated the occurrence of the interior turbulent mixing as indicated by shear instabilities,above the Equatorial Undercurrent(EUC)core at three equatorial sites along 140°W,170°W,and 165°E,respectively,based mainly on data from the Tropical Atmosphere and Ocean(TAO)mooring array.We found that turbulent mixing bursts persisted in the thermocline of all three sites.Specifically,the interior turbulent mixing layers(ITMLs)could occur in probability of approximately 68%,53%,and 48%at the three sites,respectively.The overall occurrence probability shows obvious and similar biannual variations at 140°W and 170°W,which is higher in boreal from late summer to winter and lower in spring.Vertically,the ITMLs are primarily located above the EUC core and prevail in deeper(shallower)layers from late summer to winter(spring).Most ITMLs(70%)lasted for hours to 3 days,and a few of them(15%)for more than 7 days.The thicknesses of ITMLs were concentrated between 15 and 55 m.At 165°E,the vertical distribution of ITML occurrence probability was different from that at 140°W and 170°W,as it did not show a preference for depths;the durations of ITMLs are short(also from hours to several days)and their thicknesses were between 5 and 25 m.These properties,particularly the high occurrence probability,and short durations demonstrated the persistence of thermocline mixing in the western to eastern equatorial Pacific thermocline and confirmed the generation mechanism by persistent equatorial waves as well.
文摘The shift of shock position for a class of nonlinear singularly perturbed problems is considered using a special and simple method. The location of the shock wave will be larger moved, even from interior layer to the boundary layer when the boundary conditions change smaller.
