Solvability of Nonlinear Goursat Type Problem for Hyperbolic Equation with Integral Condition

Document Type : Original Article

Authors

Taki Eddine Oussaeif ¹

Abdelfatah Bouziani ²

¹ Department of Mathematics and Informatics., The Larbi Ben M'hidi University, Oum El Bouaghi, Algeria.

² Département de Mathématiques et Informatique, Université Larbi Ben M'hidi, Oum El Bouagui, B.P. 565, 04000, Algerie.

10.22034/kjm.2018.65161

Abstract

This paper is concerned with the existence and uniqueness of a strong solution for linear problem by using a functional analysis method, which is based on an energy inequality and the density of the range of the operator generated by the problem. Applying an iterative process based on results obtained from the linear problem, we prove the existence and
uniqueness of the weak generalized solution of nonlinear hyperbolic Goursat problem with integral condition.

Keywords

Energy inequality

Goursat equation

nonlinear hyperbolic problems

integral condition

a priori estimate

Subjects

• 35 Partial differential equations

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