Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation

被引：39

作者：

Meyer, Stefan ^{[1
]}

Wilke, Mathias ^{[1
]}

机构：

[1] Univ Halle Wittenberg, Math Inst, Naturwissenschaftliche Fak 2, D-06099 Halle, Germany

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2011年 / 64卷 / 02期

关键词：

Westervelt equation; Optimal regularity; Quasilinear parabolic system; Exponential stability;

D O I：

10.1007/s00245-011-9138-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate an initial-boundary value problem for the quasilinear Westervelt equation which models the propagation of sound in fluidic media. We prove that, if the initial data are sufficiently small and regular, then there exists a unique global solution with optimal L (p) -regularity. We show furthermore that the solution converges to zero at an exponential rate as time tends to infinity. Our techniques are based on maximal L (p) -regularity for abstract quasilinear parabolic equations.

引用

页码：257 / 271

页数：15

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