J. Nonl. Evol. Equ. Appl. 2015 (3), pp. 31-45, published on June 27, 2015:

Solvability of nonlinear viscosity equation with a boundary integral condition

Taki-Eddine Oussaeif, Abdelfatah Bouziani

Department of Mathematics and Informatics, Larbi Ben Míhidi University, Oum El Bouaghi 04000, Algeria

Received on December 8, 2014, revised version on February 24 & March 13, 2015
Accepted on March 16, 2015

Communicated by Michael Ruzhansky

Abstract.  The aim of this paper is to investigate a general nonlinear hyperbolic equation with nonlocal condition. we first recall the theorems ofexistence, uniqueness and continuous dependence of a strong solution for the linear problem in [Bouziani 2002]. Then by using a priori estimate and applying an iterative process based on results obtained for the linear problem, we prove the existence, uniqueness and continuous dependence of the weak generalized solution of the nonlinear problem.
Keywords:Nonlinear viscosity equation, integral condition, strong solution, energy inequality.
2010 Mathematics Subject Classification:   35L20, 35L70, 35B45, 35D05, 35B30.

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