20-45 Vitali Vougalter

On the solvability in the sense of sequences for some non Fredholm operators with drift and anomalous diffusion (172K, pdf) May 30, 20

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Abstract. We study the solvability of certain linear nonhomogeneous elliptic equations and establish that under some technical conditions the convergence in L^2 of their right sides yields the existence and the convergence in the appropriate Sobolev space of the solutions. The problems involve the differential operators with or without Fredholm property, in particular the one dimensional negative Laplacian in a fractional power, on the whole real line or on a finite interval with periodic boundary conditions. We prove that the transport term contained in these equations provides the regularization of the solutions.

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