On the well-posedness of the Cauchy problem for a class of Pseudo-differential parabolic equations

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Title: On the well-posedness of the Cauchy problem for a class of Pseudo-differential parabolic equations
Authors: Delgado Valencia, JC
Item Type: Artefact
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-H\"ormander calculus. We establish regularity estimates, existence and uniqueness in the scale of Sobolev spaces $H(m,g)$ adapted to the corresponding H\"ormander classes. Some examples are included for fractional parabolic equations and degenerate parabolic equations.
Issue Date: 1-Feb-2018
URI: http://hdl.handle.net/10044/1/63514
DOI: https://dx.doi.org/10.1007/s00020-018-2432-z
Copyright Statement: © 2018 The Author(s). Open Access. This 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.
Keywords: Science & Technology
Physical Sciences
Mathematics
Degenerate parabolic equation
Fractional diffusion
Nonhomogeneous calculus
Microlocal analysis
WEYL-HORMANDER CALCULUS
OPERATORS
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
General Mathematics
Conference Place: Imperial College London
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences



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