Electronic Journal of Differential Equations,
Vol. 1997(1997), No. 06, pp 1-11.
Title: On a mixed problem for a coupled nonlinear system
Authors: M. R. Clark (Univ. Federal da Paraiba, Brasil)
O. A. Lima (Univ. Estadual da Paraiba, Brasil)
Abstract:
In this article we prove the existence and uniqueness of solutions to
the mixed problem associated with the nonlinear system
$$
u_{tt}-M(\int_\Omega |\nabla u|^2dx)\Delta u+|u|^\rho u+\theta =f $$
$$ \theta _t -\Delta \theta +u_{t}=g
$$
where $M$ is a positive real function, and $f$ and $g$ are known real
functions.
Submitted November 26, 1996. Published March 6, 1997.
Math Subject Classification: 35M10.
Key Words: Mixed problem; nonlinear system; weak solutions; uniqueness.