Existence and high regularity of the solution of a nonlinear parabolic problem with algebraic‐differential boundary conditions

In this paper we investigate a nonlinear 1D parabolic problem with algebraic‐differential boundary conditions. Existence, uniqueness and higher regularity of the solution is proved. It is shown that actually any regularity can be obtained provided that appropriate smoothness of the data and compatibility assumptions are required. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)