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

We prove existence, uniqueness and exponential decay of solutions to the mixed problem $$u''(x,t)-mu(t)Delta u(x,t)+sum_{i=1}^n {partial hetaoverpartial x_i}(x,t)=0 $$ $$ heta'(x,t)-Delta heta(x,t) +sum_{i=1}^n {partial u'overpartial x_i}(x,t)=0,,$$ with a suitable boundary dampi...

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Bibliographic Details
Published in:Electronic journal of differential equations 1998-02, Vol.1998 (4), p.1-20
Main Authors: H. R. Clark, L. P. San Gil Jutuca, M. Milla Miranda
Format: Article
Language:English
Subjects:
Boundary damping
Exponential stability
Mixed problem
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Summary:We prove existence, uniqueness and exponential decay of solutions to the mixed problem $$u''(x,t)-mu(t)Delta u(x,t)+sum_{i=1}^n {partial hetaoverpartial x_i}(x,t)=0 $$ $$ heta'(x,t)-Delta heta(x,t) +sum_{i=1}^n {partial u'overpartial x_i}(x,t)=0,,$$ with a suitable boundary damping, and a positive real-valued function $mu$.
ISSN:1072-6691