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 |
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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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