Electron. J. Differential Equations, Vol. 2017 (2017), No. 277, pp. 1-11.

Nonlinear singular hyperbolic initial boundary value problems

Said Mesloub, Imed Bachar

Abstract:
In this article, we aim to prove the well posedness of a one point initial boundary value problem for a nonlinear hyperbolic singular integro-differential partial differential equation. Our proofs are mainly based on a fixed point theorem and some a priori bounds. The solvability of the problem is proved when the given data are related to a weighted Sobolev space. An additional result may allow us to study the regularity of the solution.

Submitted May 10 2017. Published November 8, 2017.
Math Subject Classifications: 35L10, 35L20, 35L70.
Key Words: Fixed point theorem, a priori bound, existence and uniqueness, integro-differential equation.

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Said Mesloub
King Saud University
College of sciences Department of Mathematics
P.O. Box 2455, Riyadh 11451, Saudi Arabia
email: mesloubs@yahoo.com
Imed Bachar
King Saud University
College of sciences Department of Mathematics
P.O. Box 2455, Riyadh 11451, Saudi Arabia
email: abachar@ksu.edu.sa

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