02-399 Kaiser H.-Ch., Neidhardt H., Rehberg J.
Classical solutions of quasilinear parabolic systems on two dimensional domains (531K, Postscript) Sep 24, 02
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Abstract. Using a classical theorem of Sobolevskii on equations of parabolic type in a Banach space and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems in diagonal form admit a local, classical solution in the space of p-integrable functions, for some p greater than 1, over a bounded two dimensional space domain. As applications we have in mind systems of reaction diffusion equations, e.g. van Roosbroeck's system. The treatment of such equations in a space of integrable functions enables us to define the normal component of the flow across any part of the Dirichlet boundary by Gauss' theorem.

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