Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 1, Pages 43-67
Existence of a solution of a Fourier nonlocal quasilinear parabolic problem
Florida Institute of Technology, Department of Applied Mathematics, 150 W. University Blvd., Melbonrne 32901, Florida, USA
Received 1 February 1991; Revised 1 April 1991
Copyright © 1992 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.
The aim of this paper is to give a theorem about the existence
of a classical solution of a Fourier third nonlocal quasilinear parabolic
problem. To prove this theorem, Schauder's theorem is used. The paper
is a continuation of papers - and the generalizations of some results
from -. The theorem established in this paper can be applied to
describe some phenomena in the theories of diffusion and heat conduction
with better effects than the analogous classical theorem about the
existence of a solution of the Fourier third quasilinear parabolic problem.