TY - GEN A1 - Kaiser, Hans-Christoph A1 - Neidhardt, Hagen A1 - Rehberg, Joachim T1 - Classical solutions of quasilinear parabolic systems on two dimensional domains N2 - 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. KW - Partial differential equations KW - quasilinear parabolic systems KW - nonsmooth domains KW - mixed boundary conditions KW - discontinuous coefficients KW - local classical solutions KW - reaction-diffusion systems Y1 - 2008 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/458 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4589 ER -