International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 6, Pages 327-338
doi: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 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
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.