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International Journal of Mathematics and Mathematical Sciences
Volume 30, Issue 6, Pages 327-338
http://dx.doi.org/10.1155/S0161171202004167

Initial-boundary value problem with a nonlocal condition for a viscosity equation

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

Received 9 October 1999

Copyright © 2002 Hindawi Publishing Corporation. 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

This paper deals with the proof of the existence, uniqueness, and continuous dependence of a strong solution upon the data, for an initial-boundary value problem which combine Neumann and integral conditions for a viscosity equation. The proof is based on an energy inequality and on the density of the range of the linear operator corresponding to the abstract formulation of the studied problem.