Around a singular solution of a nonlocal nonlinear heat equation
Analysis of PDEs
2018-07-11 v1
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 pointwisely 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
Cite
@article{arxiv.1807.03567,
title = {Around a singular solution of a nonlocal nonlinear heat equation},
author = {Piotr Biler and Dominika Pilarczyk},
journal= {arXiv preprint arXiv:1807.03567},
year = {2018}
}
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20 pages