The critical Gelfand equation with singular initial data

Speaker(s)

Mikołaj Sierżęga

Date

Dec. 10, 2015, 12:30 p.m.

Room

room 4060

Seminar

Seminar of Mathematical Physics Equations Group

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The Gelfand equation is a semilinear heat equation with an exponential nonlinearity encountered e.g. in the mathematical theory of combustion. In my talk I will address the problem of existence of smooth solutions for unbounded initial data and offer a description of the critical balance between the "singularity" of the data and the growth of the nonlinearity that marks the borderline between the well-posed and the ill-posed cases. The techniques offer near sharp results and at the same time they are simple and apply to more general models that involve convex source terms. 

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