descriptionPublicationkeyboard_double_arrow_right Article 12 Jan 2010 English Publisher:Springer Science and Business Media LLCJournal:Journal of Evolution Equations, volume 10, pages 319-339 (issn: 1424-3199, eissn: 1424-3202,

Authors: Tomasz Jakubowski; Tomasz Jakubowski; Karol Szczypkowski;

doi: 10.1007/s00028-009-0051-5

Time-dependent gradient perturbations of fractional Laplacian

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Abstract

We construct a fundamental solution of the equation {\partial_t - \Delta^{\alpha/2} - b(\cdot, \cdot) \cdot\nabla_{x} = 0} for TeX{\alpha \in (1, 2)} and b satisfying a certain integral space-time condition. We also show it has α-stable upper and lower bounds.

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Keywords

[MATH] Mathematics [math], Analysis

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