# American Institute of Mathematical Sciences

2011, 2011(Special): 1319-1328. doi: 10.3934/proc.2011.2011.1319

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

 1 Department of Mathematics, Millersville University of Pennsylvania, Millersville, PA 17601, United States

Received  July 2010 Revised  April 2011 Published  October 2011

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 $n$.
Citation: Zhoude Shao. Existence and continuity of strong solutions of partly dissipative reaction diffusion systems. Conference Publications, 2011, 2011 (Special) : 1319-1328. doi: 10.3934/proc.2011.2011.1319
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