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Journal Articles Analysis and Mathematical Physics Year : 2021

Solvability of some integro-differential equations with anomalous diffusion and transport

Abstract

The article deals with the existence of solutions of an integro-differential equation in the case of anomalous diffusion with the negative Laplace operator in a fractional power in the presence of the transport term. The proof of existence of solutions is based on a fixed point technique. Solvability conditions for elliptic operators without the Fredholm property in unbounded domains are used. We discuss how the introduction of the transport term impacts the regularity of solutions.
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Dates and versions

hal-03379108 , version 1 (14-10-2021)

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Vitali Vougalter, Vitaly Volpert. Solvability of some integro-differential equations with anomalous diffusion and transport. Analysis and Mathematical Physics, 2021, 11, pp.1-26. ⟨10.1007/s13324-021-00571-8⟩. ⟨hal-03379108⟩
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