EXPONENTIAL BOUNDARY STABILIZATION FOR NONLINEAR WAVE EQUATIONS WITH LOCALIZED DAMPING AND NONLINEAR BOUNDARY CONDITION

被引：4

作者：

Taniguchi, Takeshi ^{[1
]}

机构：

[1] Kurume Univ, Grad Sch Comparat Culture, Div Math Sci, Kurume, Fukuoka 8398502, Japan

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2017年 / 16卷 / 05期

基金：

日本学术振兴会;

关键词：

Wave equation; exponential behavior of solutions; nonlinear boundary condition; ASYMPTOTIC STABILITY; SOURCE TERMS; GLOBAL EXISTENCE;

D O I：

10.3934/cpaa.2017075

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let D subset of R-d be a bounded domain in the d-dimensional Euclidian space Rd with smooth boundary Gamma = partial derivative D. In this paper we consider exponential boundary stabilization for weak solutions to the wave equation with nonlinear boundary condition: {u(tt)(t) - rho(t)Delta u(t) + b(x)u(t)(t) = f(u(t)), u(t) - 0 on Gamma(0) x (0,T), partial derivative u(t)/partial derivative v + gamma(u(t)(t)) - 0 on Gamma(1) x (0,T), u(0) - u(0),u(t)(0) - u1, where parallel to u(0)parallel to < lambda(beta) E(0) < d(beta), where lambda(beta), d(beta) are defined in (21), (22) and Gamma= Gamma(0) boolean OR Gamma(1)and Gamma(0) boolean AND Gamma(1) = phi.

引用

页码：1571 / 1585

页数：15

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