Blow-up for a nonlinear PDE with fractional Laplacian and singular quadratic nonlinearity
Analysis of PDEs
2022-09-07 v2
Abstract
We consider a parabolic-type PDE with a diffusion given by a fractional Laplacian operator and with a quadratic nonlinearity of the 'gradient' of the solution, convoluted with a singular term b. Our first result is the well-posedness for this problem: We show existence and uniqueness of a (local in time) mild solution. The main result is about blow-up of said solution, and in particular we find sufficient conditions on the initial datum and on the term b to ensure blow-up of the solution in finite time.
Cite
@article{arxiv.2007.04588,
title = {Blow-up for a nonlinear PDE with fractional Laplacian and singular quadratic nonlinearity},
author = {Diego Chamorro and Elena Issoglio},
journal= {arXiv preprint arXiv:2007.04588},
year = {2022}
}