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Article Dans Une Revue Mathematical News / Mathematische Nachrichten Année : 2022

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

Elena Issoglio
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Résumé

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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Dates et versions

hal-02893538 , version 1 (08-07-2020)
hal-02893538 , version 2 (17-07-2020)

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Citer

Diego Chamorro, Elena Issoglio. Blow-up for a nonlinear PDE with fractional Laplacian and singular quadratic nonlinearity. Mathematical News / Mathematische Nachrichten, 2022, 295, pp.1462-1479. ⟨hal-02893538v2⟩
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