Electron. J. Diff. Eqns., Vol. 1998(1998), No. 04, pp. 1-20.

On a mixed problem for a linear coupled system with variable coefficients

H. R. Clark , L. P. San Gil Jutuca, & M. Milla Miranda

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.

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H. R. Clark
Universidade Federal Fluminense, RJ, Brazil
e-mail: ganhrc@vm.uff.br
L. P. San Gil Jutuca
Universidade do Rio de Janeiro, RJ, Brazil
e-mail: rsangil@iq.ufrj.br
M. Milla Miranda
Universidade Federal do Rio de Janeiro, RJ, Brazil;
Instituto de Matematica; CP 68530 - CEP 21949-900

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