## Journal of Applied Mathematics

### On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations

Said Mesloub

#### Abstract

This paper is devoted to the study of the well-posedness of an initial boundary value problem for an odd higher order nonlinear pseudohyperbolic integrodifferential partial differential equation. We associate to the equation n nonlocal conditions and $n+1$ classical conditions. Upon some a priori estimates and density arguments, we first establish the existence and uniqueness of the strongly generalized solution in a class of a certain type of Sobolev spaces for the associated linear mixed problem. On the basis of the obtained results for the linear problem, we apply an iterative process in order to establish the well-posedness of the nonlinear problem.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 464205, 12 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305830

Digital Object Identifier
doi:10.1155/2014/464205

Mathematical Reviews number (MathSciNet)
MR3226310

#### Citation

Mesloub, Said. On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations. J. Appl. Math. 2014 (2014), Article ID 464205, 12 pages. doi:10.1155/2014/464205. https://projecteuclid.org/euclid.jam/1425305830

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