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arXiv · 2007.04588

Blow-up for a nonlinear PDE with fractional Laplacian and singular quadratic nonlinearity

Diego Chamorro·Elena Issoglio
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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.

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Diego Chamorro, Elena Issoglio. 2020-07-09. Blow-up for a nonlinear PDE with fractional Laplacian and singular quadratic nonlinearity. https://doi.org/10.1002/mana.202000480

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