High Regularity of the Solution of a Nonlinear Parabolic Boundary-Value Problem
Wendland, Wolfgang L.
Southwest Texas State University, Department of Mathematics
The aim of this paper is to report some results concerning high regularity of the solution of a nonlinear parabolic problem with a linear parabolic differential equation in one spatial dimension and nonlinear boundary conditions. We show that any regularity can be reached provided that appropriate smoothness of the data and compatibility assumptions are required.
Parabolic equation, Nonlinear boundary conditions, Maximal monotone operator, Subdifferential, Compatibility conditions
Barbu, L., Morosanu, G., & Wendland, W. L. (2002). High regularity of the solution of a nonlinear parabolic boundary-value problem. <i>Electronic Journal of Differential Equations, 2002</i>(48), pp. 1-12.