Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 1, Pages 65-79
doi:10.1155/S1048953390000065
Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with integrals
Department of Applied Mathematics, Florida Institute of Technology, 150 West University Boulevard, Melbourne, Florida 32901-6988, USA
Received 1 October 1989; Revised 1 January 1990
Copyright © 1990 Ludwik Byszewski. 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.
Abstract
In [4] and [5], the author studied strong maximum principles for nonlinear parabolic
problems with initial and nonlocal inequalities, respectively. Our purpose here is to extend
results in [4] and [5] to strong maximum principles for nonlinear parabolic problems with
nonlocal inequalities together with integrals. The results obtained in this paper can be
applied in the theories of diffusion and heat conduction, since considered here integrals in
nonlocal inequalities can be interpreted as mean amounts of the diffused substance or mean
temperatures of the investigated medium.