Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 04, pp. 1-20.
Title: On a mixed problem for a linear coupled system with variable coefficients
Authors: H. R. Clark (Univ. Federal Fluminense, RJ Brazil)
L. P. San Gil Jutuca (Univ. do Rio de Janeiro, Brazil)
M. Milla Miranda (Univ. Federal do Rio de Janeiro, Brazil)
Abstract:
We prove existence, uniqueness and exponential decay of solutions to the mixed
problem
$$u''(x,t)-\mu(t)\Delta u(x,t)+\sum_{i=1}^n
{\partial \theta\over\partial x_i}(x,t)=0 $$
$$ \theta'(x,t)-\Delta \theta(x,t) +\sum_{i=1}^n
{\partial u'\over\partial x_i}(x,t)=0\,,$$
with a suitable boundary damping, and a positive real-valued function $\mu$.
Submitted August 24, 1997. Published February 13, 1998.
Math Subject Classification: 35F15, 35N10, 35B40.
Key Words: Mixed problem; Boundary damping; Exponential stability.