PageHeader : Funkcialaj Ekvacioj, 41 (1998) 271-289
Title : On Solvabih.ty and Stabih.ty of Solutions of Nonlinear Degenerate
Title : Hyperboh.c Equations with Boundary Damping
AuthorInfo : By
AuthorInfo : M. M. CAVALCANTI,1 N. A. LAR'KIN2 and J. A. SORIANO1
AuthorInfo : (Univ. Estadual de Maringa1, Brasil, and Inst. of Theor. and App. Mechanics, Russia)
section : 1. Inffoduction
section : 2. Notations and main results We define (2. 1) V $=$ { v $\in H^{1}$ ( $\Omega);$ v $=0$ on $\Gamma_{1}$ } which is the Hilbert space. We denote (u, $ v)=\int_{\Omega}u(x)v(x)dx$ and $||u||_{\infty}=\mathrm{e}\mathrm{s}\mathrm{s}\sup_{t\geq 0}||u(t)||_{L^{\infty}(\Omega)}$ , $u^{\prime}=\frac{\partial u}{\partial t}$ , $F(Vu)=F(u_{x_{1^{ }}},\ldots, u_{x_{n}})$ , (u, $ v)_{\Gamma_{0}}=\int_{\Gamma_{0}}u(x)v(x)d\Gamma$ .
section : 3. Strong solutions
subsection : The First Estimate
subsection : The Second Estimate
subsection : Analysis of the Nonh.near Term
section : 4. Asymptotic behaviour
section : References