Journal of Inequalities and Applications
Volume 5 (2000), Issue 5, Pages 467-486
A qualitative theory for parabolic problems under dynamical boundary conditions
LMPA Joseph Liouville, EA 2597, Université du Littoral Côte d'Opale, 50, rue F. Buisson, B.P. 699, Calais Cedex F-62228, France
Received 16 July 1999; Revised 13 September 1999
Copyright © 2000 Joachim von Bellow and Colette de Coster. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
For nonlinear parabolic problems in a bounded domain under dynamical boundary conditions, general comparison techniques are established similar to the ones under Neumann or Dirichlet boundary conditions. In particular, maximum principles and basic a priori estimates are derived, as well as lower and upper solution techniques that lead to functional band type estimates for classical solutions. Finally, attractivity properties of equilibria are discussed that also illustrate the damping effect of the dissipative dynamical boundary condition.