On the well-posedness of the Cauchy problem for a class of Pseudo-differential parabolic equations
File(s)Delgado2018_Article_OnTheWell-PosednessForAClassOf.pdf (535.79 KB)
Published version
Author(s)
Delgado Valencia, JC
Type
Journal Article
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.
Date Issued
2018-02-01
Date Acceptance
2018-01-11
Citation
Integral Equations and Operator Theory, 2018, 90 (1)
ISSN
0378-620X
Publisher
Springer Verlag
Journal / Book Title
Integral Equations and Operator Theory
Volume
90
Issue
1
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.
Publication Status
Published
Coverage Spatial
Imperial College London
Article Number
3
Date Publish Online
2018-02-28