On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations
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 esti...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/464205 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |