Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations

V. Kolokoltsov; M. Veretennikova

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arXiv · 1402.6735

Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations

V. Kolokoltsov·M. Veretennikova

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Abstract

The purpose is to study the Cauchy problem for non-linear in time and space pseudo-differential equations. These include the fractional in time versions of HJB equations governing the controlled scaled CTRW. As a preliminary step which is of independent interest we analyse the corresponding linear equation proving its well-posedness and smoothing properties.

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V. Kolokoltsov, M. Veretennikova. 2014-02-26. Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations. https://arxiv.org/abs/1402.6735

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