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

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 $n$.