Convergence to nonlinear diffusion waves for solutions of p-system with time-dependent damping

被引：29

作者：

Li, Haitong ^{[1
]}

Li, Jingyu ^{[1
]}

Mei, Ming ^{[2
,3
]}

Zhang, Kaijun ^{[1
]}

机构：

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

[2] Champlain Coll St Lambert, Dept Math, St Lambert, PQ J4P 3P2, Canada

[3] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 456卷 / 02期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

Time-dependent damping; Nonlinear diffusion waves; Convergence rates; Time-weighted energy estimates; COMPRESSIBLE EULER EQUATIONS; HYPERBOLIC CONSERVATION-LAWS; BOUNDARY VALUE-PROBLEM; ASYMPTOTIC-BEHAVIOR; RATES; FLOW; DISSIPATION; EXISTENCE;

D O I：

10.1016/j.jmaa.2017.07.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the Cauchy problem for the hyperbolic p-system with time gradually-degenerate damping term -1/(1+t)(lambda)u for 0 <= lambda < 1, and show that the damped p-system has a couple of global solutions uniquely, and such solutions tend time-asymptotically to the shifted nonlinear diffusion waves, which are the solutions of the corresponding nonlinear parabolic equation governed by the Darcy's law. We further derive the convergence rates when the initial perturbations are in L-2. The approach adopted is the technical time-weighted energy method. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：849 / 871

页数：23

共 47 条

[1]

DAFERMOS CM, 1995, Z ANGEW MATH PHYS, V46, pS294

[2] Initial-boundary value problem for p-system with damping in half space [J].

Deng, Shijin .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 143 :193-210

[3] Theory of damped wave models with integrable and decaying in time speed of propagation [J].

Ebert, Marcelo Rempel ;

Reissig, Michael .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2016, 13 (02) :417-439

[4]

Geng S., 2010, PARTIAL DIFFERENTIAL, V36, P850

[5] Lp-convergence rates to nonlinear diffusion waves for quasilinear equations with nonlinear damping [J].

Geng, Shifeng ;

Zhang, Lina .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (01) :31-50

[6]

Hou F., 2015, ARXIV151004613

[7]

Hou F., 2016, ARXIV160608935V1

[8] Construction and qualitative behavior of the solution of the perturbated Riemann problem for the system of one-dimensional isentropic flow with damping [J].

Hsiao, L ;

Tang, SQ .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 123 (02) :480-503

[9] Initial boundary value problem for the system of compressible adiabatic flow through porous media [J].

Hsiao, L ;

Pan, RH .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 159 (01) :280-305

[10] Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media [J].

Hsiao, L ;

Luo, T .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 125 (02) :329-365

← 1 2 3 4 5 →