On a nonlinear system containing nonlocal terms related to a fluid flow model

Á. Besenyei, L. Eötvös University, Budapest, Hungary

E. J. Qualitative Theory of Diff. Equ., Proc. 8'th Coll. Qualitative Theory of Diff. Equ., No. 3. (2008), pp. 1-13.

Abstract: We consider a nonlinear system of differential equations where the main parts may contain nonlocal dependence on the unknowns. This system is a generalization of a model describing fluid flow in porous medium. Existence of weak solutions, boundedness and stabilization of solutions as $t\to\infty$ is shown by using the theory of monotone operators, and some examples are given.

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