abstract

ABSTRACT

GLOBAL BEHAVIOR OF SOLUTIONS OF THE BRINKMAN-FORCHHEIMER EQUATIONS

Ugurlu, Davut
Ph.D., Department of Mathematics
Supervisor: Prof. Dr. Okay €elebi
Co-Supervisor: Prof. Dr. Varga Kalantarov

December 2001, 83 pages.

In this thesis, we study the existence, uniqueness and continuous dependence of solutions on the coefficients $\gamma$ and

for the Brinkman-Forchheimer equations which are given by

$\begin{displaymath}u_t=\gamma \Delta u-au-b \mid u \mid^\alpha u- \nabla p, \quad x \in \Omega, \quad t >0\end{displaymath}$

$\begin{displaymath}\mbox{div} \; u=0, \quad x \in \Omega, \quad t >0\end{displaymath}$

with the initial

$\begin{displaymath}u(x,0)=u_0(x), \qquad x \in \Omega\end{displaymath}$

and boundary conditions

$\begin{displaymath}u(x,t)=0, \quad x \in \partial \Omega, \quad t >0\end{displaymath}$

where $\Omega \subset {\R}^n$ is a bounded domain with sufficiently smooth boundary $\partial \Omega$ . Furthermore, the existence of determining functionals of the above problem is proved.
Keywords: Structural Stability, Porous Medium, Continuous Dependence on the Coefficients, Determining Functionals.