Existence and uniqueness of the solutions to convection-diffusion equations

Alireza Ataei

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arXiv · 2310.20269

Existence and uniqueness of the solutions to convection-diffusion equations

Alireza Ataei

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Abstract

In this work, we study convection-diffusion equations in the cases of bounded drifts and drifts induced by the gradient of a potential. We define a new notion of solution and prove its existence and uniqueness. Furthermore, we show the conservation of mass, the convergence to the initial data, and the strong maximum principle.

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Alireza Ataei. 2023-10-31. Existence and uniqueness of the solutions to convection-diffusion equations. https://arxiv.org/abs/2310.20269

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