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Solvability of nonlinear hyperbolic equation with nonlinear integral Neumann conditions
by Oussaeif Taki-Eddine   Chebana Zainouba   Ouannas Adel

Vol. 17 No. 3 (2022) P.333~P.354
 DOI: https://doi.org/10.21915/BIMAS.2022303 10.21915/BIMAS.2022303

ABSTRACT

In this paper, we examine a nonlinear hyperbolic equation with a nonlinear integral condition, where we prove the existence and the uniqueness of the linear problem by the Faedo-Galerkin method. By applying an iterative process to some significant results obtained for the linear problem, the existence and the uniqueness of the weak solution for the nonlinear problem are additionally examined.

KEYWORDS
Hyperbolic equation, nonlinear integral condition, Faedo-Galerkin method, existence

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35D30, 35L05, 35L70

MILESTONES