Articles

CONVERGENCE RATES TO NONLINEAR DIFFUSIVE WAVES FOR SOLUTIONS TO NONLINEAR HYPERBOLIC SYSTEM

  • Shifeng GENG ,
  • Yanjuan TANG
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  • School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Received date: 2017-12-05

  Revised date: 2018-07-13

  Online published: 2019-03-13

Supported by

The first author was supported by the National Natural Science Foundation of China (11701489, 11871412), the Hunan Provincial Natural Science Foundation of China (2018JJ2373, 2018JJ3481).

Abstract

This article is involved with the asymptotic behavior of solutions for nonlinear hyperbolic system with external friction. The global existence of classical solutions is proven, and Lp convergence rates are obtained. Compared with the results obtained by Hsiao and Liu, better convergence rates are obtained in this article.

Cite this article

Shifeng GENG , Yanjuan TANG . CONVERGENCE RATES TO NONLINEAR DIFFUSIVE WAVES FOR SOLUTIONS TO NONLINEAR HYPERBOLIC SYSTEM[J]. Acta mathematica scientia, Series B, 2019 , 39(1) : 46 -56 . DOI: 10.1007/s10473-019-0105-x

References

[1] Cao W, Huang F, Li T, et al. Global entropy solutions to an inhomogeneous isentropic compressible Euler system. Acta Math Sci, 2016, 36B:1215-1224
[2] Geng S, Zhang L. Lp-convergence rates to nonlinear diffusion waves for quasilinear equations with nonlinear damping. Z Angew Math Phys, 2015, 66:31-50
[3] He C, Huang F, Yong Y. Stability of planar diffusion wave for nonlinear evolution equation. Science China Mathematics, 2012, 55:337-352
[4] Hsiao L, Liu T. Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping. Comm Math Phys, 1992, 143:599-605
[5] Hsiao L, Liu T. Nonlinear diffusion phenomena of nonlinear hyperbolic system. Chin Ann Math, Ser B, 1993, 14:465-480
[6] Ma H, Mei M. Best asymptotic profile for linear damped p-system with boundary effect. J Differential Equations, 2010, 249:446-484
[7] Marcati P, Mei M, Rubino B. Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping. J Math Fluid Mech, 2005, 7:S224-S240
[8] Marcati P, Nishihara K. The Lp-Lq estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media. J Differential Equations, 2003, 191:445-469
[9] Matsumura A. Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipation. Publ RIMS, Kyoto Univ, 1977, 13:349-379
[10] Mei M. Nonlinear diffusion waves for hyperbolic p-system with nonlinear damping. J Differential Equations, 2009, 247:1275-1296
[11] Mei M. Best asymptotic profile for hyperbolic p-system with damping. SIAM J Math Anal, 2010, 42:1-23
[12] Nishida T. Nonlinear hyperbolic equations and related topics in fluid dynamics. Publications Mathématique D' orsay 78-02, Départment de Mathématique, Université de Paris-Sud, 1978
[13] Nishihara K. Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping. J Differential Equations, 1996, 131:171-188
[14] Nishihara K. Asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping. J Differential Equations, 1997, 137:384-396
[15] Nishihara K, Wang W, Yang T. Lp-convergence rate to nonlinear diffusion waves for p-system with damping. J Differential Equations, 2000, 161:191-218
[16] Zhao H. Convergence to strong nonlinear diffusion waves for solutions of p-system with damping. J Differential Equations, 2001, 174:200-236
[17] Zhu C, Jiang M. Lp-decay rates to nonlinear diffusion waves for p-system with nonlinear damping. Sci Chin, Ser A, 2006, 49:721-739
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