International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 7, Pages 435-447
doi:10.1155/S0161171202004507

On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces

Abdelfatah Bouziani1,2

1Département de Mathématiques, Centre Universitaire Larbi Ben M'hidi-Oum El Bouagui, B.P. 565, 04000, Algeria
2Mathematical Division, The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, Trieste 34100, Italy

Received 11 January 2000

Copyright © 2002 Abdelfatah Bouziani. 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

The aim of this paper is to prove the existence, uniqueness, and continuous dependence upon the data of a generalized solution for certain singular parabolic equations with initial and nonlocal boundary conditions. The proof is based on an a priori estimate established in nonclassical function spaces, and on the density of the range of the operator corresponding to the abstract formulation of the considered problem.