Existence and Boundary Stabilization of a Nonlinear Hyperbolic Equation with Time-dependent Coefficients
Date
1998-03-10
Authors
Cavalcanti, Marcelo M.
Domingos Cavalcanti, V. N.
Soraino, J. A.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In this article, we study the hyperbolic problem
K(x, t)u>tt - ∑nj=1 (α(x, t) uxj) + F(x, t, u, ∇u) = 0
u = 0 on Γ1, ∂u / ∂v + β(x)ut = 0 on Γ0
u(0) = u0, ut(0) = u1 in Ω,
where Ω is a bounded region in ℝn whose boundary is partitioned into two disjoint sets Γ0, Γ1. We prove existence, uniqueness, and uniform stability of strong and weak solutions when the coefficients and the boundary conditions provide a damping effect.
Description
Keywords
Boundary stabilization, Asymptotic behaviour
Citation
Cavalcanti, M. M., Domingos Cavalcanti, V. N., & Soriano, J. A. (1998). Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients. <i>Electronic Journal of Differential Equations, 1998</i>(08), pp. 1-21.
Rights
Attribution 4.0 International