Blow-up patterns for the Fujita equation

Prelegent(ci)

Mikołaj Sierżęga

Termin

27 października 2016 12:30

Pokój

p. 4060

Seminarium

Seminarium Zakładu Równań Fizyki Matematycznej

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The Fujita equation (a semilinear heat equation with a power type nonlinearity) is among the simplest and the most thoroughly studied non-linear parabolic PDEs. Put forward in the sixties, it has been a canonical case study of the singularity formation ever since. Despite its apparent simplicity it displays a staggering complexity of blow-up dynamics much of which remains unexplored. In particular, the description of blow-up in the so-called Sobolev supercritical regime poses a challenge that calls for new insights and methods.
In my talk I will describe the intricacies of the singularity formation for this model, outline what's known, what's fresh and what's conjectural and present some important open problems.

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