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Measure-valued solutions of nonlinear parabolic equations with logarithmic diffusion

Measure-valued solutions of nonlinear parabolic equations with logarithmic diffusion We prove the existence of a Radon measure-valued solution for a class of nonlinear degenerate parabolic equations with a “logarithmic diffusion” when the initial datum u 0 is a bounded Radon measure, and we study the regularity of these solutions. In particular, we prove that a regularizing effect appears if the initial datum is diffused with respect to the “ C 2 -capacity” since in this case the solution becomes a summable function. Finally, we study the uniqueness of these measure-valued solutions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Measure-valued solutions of nonlinear parabolic equations with logarithmic diffusion

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References (34)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer Basel
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-015-0275-5
Publisher site
See Article on Publisher Site

Abstract

We prove the existence of a Radon measure-valued solution for a class of nonlinear degenerate parabolic equations with a “logarithmic diffusion” when the initial datum u 0 is a bounded Radon measure, and we study the regularity of these solutions. In particular, we prove that a regularizing effect appears if the initial datum is diffused with respect to the “ C 2 -capacity” since in this case the solution becomes a summable function. Finally, we study the uniqueness of these measure-valued solutions.

Journal

Journal of Evolution EquationsSpringer Journals

Published: Sep 1, 2015

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