On the Well-Posedness for a Class of Pseudo-Differential Parabolic Equations

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Abstract

In this work we study the well-posedness of the Cauchy problem for a class of pseudo-differential parabolic equations in the framework of Weyl–Hörmander calculus. We establish regularity estimates, existence and uniqueness in the scale of Sobolev spaces H(mg) adapted to the corresponding Hörmander classes. Some examples are included for fractional parabolic equations and degenerate parabolic equations.

Keywords

Degenerate parabolic equation Fractional diffusion Nonhomogeneous calculus Microlocal analysis 

Mathematics Subject Classification

Primary 35L80 Secondary 47G30 35L40 35A27 

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsImperial College LondonLondonUK

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