On existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:281

Article

Cavalcanti, MM ; Cavalcanti, VND ; Soriano, JA

关键词: global solvability;    boundary damping;    stabilization;    degenerate equation;   

DOI  :  10.1016/S0022-247X(02)00558-9

来源: Elsevier

【 摘 要 】

We study the global existence of solutions of the nonlinear degenerate wave equation (rho greater than or equal to 0) (*) \rho(x)y- Deltay = 0 in Ohm x ]0, infinity[, y = 0 on Gamma(1) x]0, infinity[, partial derivativey/partial derivativenu + y' + f (y) + g(y') = 0 on Gamma(0) x ]0, infinity[, y(x, 0) = y(0), (rootrhoy')(x, 0) = (rootrhoy(1))(x) in Ohm, where y' denotes the derivative of y with respect to parameter t, f(s) = C-0\s\delta(S) and g is a non-decreasing C-1 function such that k(1)\s\(xi+2) less than or equal to g(s)s less than or equal to k(2)\s\(xi+2) for some k(1), k(2) > 0 with 0 < delta, xi less than or equal to 1/ (n - 2) if n greater than or equal to 3 or delta, xi > 0 if n = 1, 2. The existence of solutions is proved by means of the Faedo-Galerkin method. Furthermore, when xi = 0 the uniform decay is obtained by making use of the perturbed energy method. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

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