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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
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.
