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 |
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| Online Access: | https://doi.org/10.1186/s42787-022-00156-9 |
| Summary: | 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). |
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| ISSN: | 2090-9128 |