FDE2 Organiser talks - Non-existence of solutions to fractional stochastic heat equations

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• Eulalia Nualart (Universitat Pompeu Fabra)
• Tuesday 25 January 2022, 09:00-09:30
• Seminar Room 2, Newton Institute.

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FDE2 - Fractional differential equations

1) Eulalia Nualart (Universitat Pompeu Fabra, Barcelona) Title: Non-existence of solutions to fractional stochastic heat equations Abstract: We consider the fractional stochastic heat equation on a bounded domain with Dirichlet boundary conditions driven by a Gaussian noise, which is white in time and has a spatial correlation in space. The equation has a locally Lipschitz drift. We show that the well-known Osgood condition is necessary for the solution to blow-up in finite time, providing the converse of a Theorem by Bonder and Groisman. We also consider the same equation on the whole space and show that the Osgood condition is sufficient for the non-existence of global solutions. This is a joint work with Mohammud Foondun (University of Strathclyde).  

This talk is part of the Isaac Newton Institute Seminar Series series.

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