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

Ludwik Byszewski

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 [1]-[8] and the generalizations of some results from [9]-[11]. 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.