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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832546013511942144 |
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| author | Said Mesloub |
| author_facet | Said Mesloub |
| author_sort | Said Mesloub |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bd6d3e6d7b9b4691ba70a4c8a31a689d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-bd6d3e6d7b9b4691ba70a4c8a31a689d2025-02-03T07:24:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/464205464205On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential EquationsSaid Mesloub0Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaThis 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.http://dx.doi.org/10.1155/2014/464205 |
| spellingShingle | Said Mesloub On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations Journal of Applied Mathematics |
| title | On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations |
| title_full | On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations |
| title_fullStr | On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations |
| title_full_unstemmed | On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations |
| title_short | On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations |
| title_sort | on an initial boundary value problem for a class of odd higher order pseudohyperbolic integrodifferential equations |
| url | http://dx.doi.org/10.1155/2014/464205 |
| work_keys_str_mv | AT saidmesloub onaninitialboundaryvalueproblemforaclassofoddhigherorderpseudohyperbolicintegrodifferentialequations |