Existence of weak solutions to a convection–diffusion equation in amalgam spaces
Abstract We consider the local existence and uniqueness of a weak solution for a convection–diffusion equation in amalgam spaces. We establish the local existence and uniqueness of solution for the initial condition in amalgam spaces. Furthermore, we prove the validity of the Fujita–Weissler critica...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-12-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s42787-022-00156-9 |
| _version_ | 1797977270191652864 |
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| author | Md. Rabiul Haque |
| author_facet | Md. Rabiul Haque |
| author_sort | Md. Rabiul Haque |
| collection | DOAJ |
| description | Abstract We consider the local existence and uniqueness of a weak solution for a convection–diffusion equation in amalgam spaces. We establish the local existence and uniqueness of solution for the initial condition in amalgam spaces. Furthermore, we prove the validity of the Fujita–Weissler critical exponent for local existence and uniqueness of solution in the amalgam function class that is identified by Escobedo and Zuazua (J Funct Anal 100:119–161, 1991). |
| first_indexed | 2024-04-11T05:04:14Z |
| format | Article |
| id | doaj.art-72a1a00850334e7cbb0731b6650d1653 |
| institution | Directory Open Access Journal |
| issn | 2090-9128 |
| language | English |
| last_indexed | 2024-04-11T05:04:14Z |
| publishDate | 2022-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-72a1a00850334e7cbb0731b6650d16532022-12-25T12:30:42ZengSpringerOpenJournal of the Egyptian Mathematical Society2090-91282022-12-0130111910.1186/s42787-022-00156-9Existence of weak solutions to a convection–diffusion equation in amalgam spacesMd. Rabiul Haque0Department of Mathematics, University of RajshahiAbstract We consider the local existence and uniqueness of a weak solution for a convection–diffusion equation in amalgam spaces. We establish the local existence and uniqueness of solution for the initial condition in amalgam spaces. Furthermore, we prove the validity of the Fujita–Weissler critical exponent for local existence and uniqueness of solution in the amalgam function class that is identified by Escobedo and Zuazua (J Funct Anal 100:119–161, 1991).https://doi.org/10.1186/s42787-022-00156-9Convection–diffusion equationsAmalgam spacesWeak solutionUniqueness |
| spellingShingle | Md. Rabiul Haque Existence of weak solutions to a convection–diffusion equation in amalgam spaces Journal of the Egyptian Mathematical Society Convection–diffusion equations Amalgam spaces Weak solution Uniqueness |
| title | Existence of weak solutions to a convection–diffusion equation in amalgam spaces |
| title_full | Existence of weak solutions to a convection–diffusion equation in amalgam spaces |
| title_fullStr | Existence of weak solutions to a convection–diffusion equation in amalgam spaces |
| title_full_unstemmed | Existence of weak solutions to a convection–diffusion equation in amalgam spaces |
| title_short | Existence of weak solutions to a convection–diffusion equation in amalgam spaces |
| title_sort | existence of weak solutions to a convection diffusion equation in amalgam spaces |
| topic | Convection–diffusion equations Amalgam spaces Weak solution Uniqueness |
| url | https://doi.org/10.1186/s42787-022-00156-9 |
| work_keys_str_mv | AT mdrabiulhaque existenceofweaksolutionstoaconvectiondiffusionequationinamalgamspaces |