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Existence and continuity of strong solutions of partly dissipative reaction diffusion systems

Pages: 1319 - 1328, Issue Special, September 2011

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Zhoude Shao - Department of Mathematics, Millersville University of Pennsylvania, Millersville, PA 17601, United States (email)

Abstract: We discuss the existence and continuity of strong solutions of partly dissipative reaction diffusion systems of the FitzHugh-Nagumo type. Under appropriate conditions, we proved the existence of strong solutions of such systems on $[0, \infty)$ using a Galerkin type of argument. Then we proved that these strong solutions are continuous with respect to initial data in the space $V \times H^1 (\Omega)$, where $V$ is a subspace of $H^1 (\Omega)$ defined according to the boundary condition imposed for the $u$- component in our system. The continuity result is independent of the spatial dimension $n$.

Keywords:  Partly dissipative reaction di usion systems, strong solutions, existence, continuity with respect to initial data
Mathematics Subject Classification:  Primary: 35A01, 35B65; Secondary:35K99

Received: July 2010;      Revised: April 2011;      Published: October 2011.