Blow up for a nonlinear PDE

Diego Chamorro (1) , Elena Issoglio (2)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
2 School of Mathematics [Leeds]

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.

Mots clés: mild solutions; singular coefficients; nonlinear PDE; blow up

Domaines: Equations aux dérivées partielles [math.AP]

Diego Chamorro, Elena Issoglio. Blow up for a nonlinear PDE. 2020. ⟨hal-02893538v1⟩