On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification
This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continu...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503210010 |
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| _version_ | 1849309396677427200 |
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| author | Abdelfatah Bouziani |
| author_facet | Abdelfatah Bouziani |
| author_sort | Abdelfatah Bouziani |
| collection | DOAJ |
| description | This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation. Next, analogous results are established for the quasilinear problem, using an iterative process based on results obtained for the linear problem. |
| format | Article |
| id | doaj-art-11b374ce7f374e5593cf31fb7bbedbe5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-11b374ce7f374e5593cf31fb7bbedbe52025-08-20T03:54:11ZengWileyAbstract and Applied Analysis1085-33751687-04092003-01-0120031057358910.1155/S1085337503210010On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specificationAbdelfatah Bouziani0Department of Mathematics, The Larbi Ben M'hidi University Centre, Oum El Bouagui 04000, AlgeriaThis paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation. Next, analogous results are established for the quasilinear problem, using an iterative process based on results obtained for the linear problem.http://dx.doi.org/10.1155/S1085337503210010 |
| spellingShingle | Abdelfatah Bouziani On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification Abstract and Applied Analysis |
| title | On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification |
| title_full | On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification |
| title_fullStr | On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification |
| title_full_unstemmed | On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification |
| title_short | On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification |
| title_sort | on the weak solution of a three point boundary value problem for a class of parabolic equations with energy specification |
| url | http://dx.doi.org/10.1155/S1085337503210010 |
| work_keys_str_mv | AT abdelfatahbouziani ontheweaksolutionofathreepointboundaryvalueproblemforaclassofparabolicequationswithenergyspecification |