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

Abdelfatah Bouziani1,2

 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

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.