Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation
This paper deals with an initial boundary value problem with an integral condition for the two-dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one-dimensional problem. Existence, uniqueness, and continuous dependence upo...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503305019 |
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| _version_ | 1832549004540379136 |
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| author | Nabil Merazga Abdelfatah Bouziani |
| author_facet | Nabil Merazga Abdelfatah Bouziani |
| author_sort | Nabil Merazga |
| collection | DOAJ |
| description | This paper deals with an initial boundary value problem with an
integral condition for the two-dimensional diffusion equation.
Thanks to an appropriate transformation, the study of the given
problem is reduced to that of a one-dimensional problem.
Existence, uniqueness, and continuous dependence upon data of a
weak solution of this latter are proved by means of the Rothe
method. Besides, convergence and an error estimate for a
semidiscrete approximation are obtained. |
| format | Article |
| id | doaj-art-0e8502f36d52406fb663898a46f454c7 |
| 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-0e8502f36d52406fb663898a46f454c72025-02-03T06:12:20ZengWileyAbstract and Applied Analysis1085-33751687-04092003-01-0120031689992210.1155/S1085337503305019Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equationNabil Merazga0Abdelfatah Bouziani1Département de Mathématiques, Centre Universitaire Larbi Ben M'hidi, Oum El Bouagui 04000, AlgeriaDépartement de Mathématiques, Centre Universitaire Larbi Ben M'hidi, Oum El Bouagui 04000, AlgeriaThis paper deals with an initial boundary value problem with an integral condition for the two-dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one-dimensional problem. Existence, uniqueness, and continuous dependence upon data of a weak solution of this latter are proved by means of the Rothe method. Besides, convergence and an error estimate for a semidiscrete approximation are obtained.http://dx.doi.org/10.1155/S1085337503305019 |
| spellingShingle | Nabil Merazga Abdelfatah Bouziani Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation Abstract and Applied Analysis |
| title | Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation |
| title_full | Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation |
| title_fullStr | Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation |
| title_full_unstemmed | Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation |
| title_short | Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation |
| title_sort | rothe method for a mixed problem with an integral condition for the two dimensional diffusion equation |
| url | http://dx.doi.org/10.1155/S1085337503305019 |
| work_keys_str_mv | AT nabilmerazga rothemethodforamixedproblemwithanintegralconditionforthetwodimensionaldiffusionequation AT abdelfatahbouziani rothemethodforamixedproblemwithanintegralconditionforthetwodimensionaldiffusionequation |