Abstract.
Using results on abstract evolutions equations and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems 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. The treatment of such equations in a space of integrable functions enables us to define the normal component of the current across the boundary of any Lipschitz subset. As applications we have in mind systems of reaction diffusion equations, e.g. van Roosbroeck’s system.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kaiser, HC., Neidhardt, H. & Rehberg, J. Classical solutions of quasilinear parabolic systems on two dimensional domains. Nonlinear differ. equ. appl. 13, 287–310 (2006). https://doi.org/10.1007/s00030-006-3028-x
Issue Date:
DOI: https://doi.org/10.1007/s00030-006-3028-x