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Around a singular solution of a nonlocal nonlinear heat equation

  • Piotr BilerEmail author
  • Dominika Pilarczyk
Open Access
Article
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Abstract

We study the existence of global-in-time solutions for a nonlinear heat equation with nonlocal diffusion, power nonlinearity and suitably small data (either compared in the pointwise sense to the singular solution or in the norm of a critical Morrey space). Then, asymptotics of subcritical solutions is determined. These results are compared with conditions on the initial data leading to a finite time blowup.

Keywords

Fractional Laplacian Nonlinear heat equation Singular solution Global-in-time solutions Singular potential Asymptotic behavior Stability 

Mathematics Subject Classification

35K55 35B05 35B40 60J60 

Notes

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© The Author(s) 2019

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.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland
  2. 2.Wydział MatematykiPolitechnika WrocławskaWrocławPoland

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