Exponential Decay of Energy for a Logarithmic Wave Equation
被引量:2
Exponential Decay of Energy for a Logarithmic Wave Equation
摘要
In this paper we consider the initial boundary value problem for a class of logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for the logarithmic wave equation with linear damping and some suitable initial data. The results extend the early results.
参考文献16
-
1Bialynicki-Birula I., Mycielski J., Wave equations with logarithmic nonlinearities. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 23(4) (1975), 461-466.
-
2Bartkowski K., Gorka P., One-dimensional Klein-Gordon equation with logarithmic nonlinearities. J Phys. A, 41(35) (2008), 355201,11 pp.
-
3Gorka P., Logarithmic Klein-Gordon equation. Acta Phys. Polon. B, 40(1) (2009), 59-66.
-
4Bialynicki-Birula I., Mycielski J., Nonlinear wave mechanics. Ann. Physics, 100(1-2) (1976), 62-93.
-
5Hiramatsu T., Kawasaki M. and Takahashi F., Numerical study of Q-ball formation in gravity mediation. Journal of Cosmology and Astroparticle Physics, 2010(6) (2010), 001-008.
-
6Cazenave T., Haraux A., Equations d'evolution avec non-linearite logarithmique. Ann. Fac. Sci. Toulouse Math., 2(1) (1980), 21-51.
-
7Han X. S., Global existence of weak solutions for a logarithmic wave equation arising from Q-ball dynamics. Bull. Korean Math. Soc., 50(1) (2013), 275-283.
-
8Levine H.A., Instability and nonexistence of global solutions to nonlinear wave equations of the form. Trans. Amer. Math. Soc., 192 (1974), 1-21.
-
9Georgiev V., Todorova G., Existence of a solution of the wave equation with nonlinear damping and source term. ]. Differential Equations, 109 (1994), 295-308.
-
10Nakao M., Decay of solutions of the wave equation with a local nonlinear dissipation. Math. Annalen, 305(1996), 403-407.
-
1张维弢,冯德兴.EXPONENTIAL DECAY DOMAIN OF ENERGY FOR WAVE EQUATION UNDER FEEDBACK CONTROL[J].Acta Mathematicae Applicatae Sinica,1999,15(3):249-256.
-
2SUN Peng.Exponential decay of expansive constants[J].Science China Mathematics,2013,56(10):2063-2067. 被引量:1
-
3Guangwu Wang.EXPONENTIAL DECAY FOR THE VISCOUS BIPOLAR QUANTUM HYDRODYNAMIC MODEL[J].Annals of Applied Mathematics,2015,31(3):329-336.
-
4ZHAO Chunshan.Remark on Exponential Decay of Ground States for N-Laplacian Equations[J].Journal of Partial Differential Equations,2009,22(1):32-41.
-
5HAN Xiaosen.Global Existence and Exponential Decay for a Nonlinear Viscoelastic Equation with Nonlinear Damping[J].Journal of Partial Differential Equations,2009,22(4):299-314. 被引量:4
-
6Shun-Tang Wu.EXPONENTIAL DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS[J].Acta Mathematica Scientia,2012,32(6):2237-2246. 被引量:2
-
7欧阳才衡.BAERNSTEIN THEOREM IN UNIT BALL OF C^n[J].Chinese Science Bulletin,1987,32(9):581-584.
-
8Yu-xia Guo, Peng-fei YaoDepartment of Mathematics, Tsinghua University, Beijing 100084, China,Institute of System Sciences. Academy of Mathematics and System Sciences, Chinese Academy of Sciences,Beijing 100080, China.On Boundary Stability of Wave Equations with Variable Coefficients[J].Acta Mathematicae Applicatae Sinica,2002,18(4):589-598.
-
9陈天平.CONVERGENCE AND ASYMPTOTIC EXPANSIONS FOR SPLINES[J].Chinese Science Bulletin,1986,31(24):1657-1661.
-
10Yong-jiang Yu,Kai-tai Li,Ai-xiang Huang.Gevrey Class Regularity and Exponential Decay Property for Navier-Stokes-α Equations[J].Acta Mathematicae Applicatae Sinica,2007,23(1):49-58. 被引量:1