Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. 197--221.

Strong bounded solutions for nonlinear parabolic systems

Nsoki Mavinga, Mubenga N. Nkashama

In this article we study the existence of strong bounded solutions for nonlinear parabolic systems on a domain which is bounded in space and unbounded in time (namely the entire real line). We use nonlinear iteration arguments combined with some a priori estimates to derive the existence results. We also provide conditions under which we have a positive solution. Some examples are given to illustrate the results.

Published February 10, 2014.
Math Subject Classifications: 35K55, 35K60.
Key Words: Nonlinear parabolic systems; nonlinear boundary conditions; Caratheodory functions; quasimonotone properties; sub and supersolutions.

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Nsoki Mavinga
Department of Mathematics and Statistics
Swarthmore College
Swarthmore, PA 19081, USA
  Mubenga N. Nkashama
Department of Mathematics
University of Alabama at Birmingham
Birmingham, AL 35294-1170, USA

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