20-108 Vitali Vougalter, Vitaly Volpert

Solvability of some integro-differential equations with anomalous diffusion and transport (217K, pdf) Dec 25, 20

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Abstract. The article deals with the existence of solutions of an integro-differential equation in the case of the 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 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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