seminar

[Pedro Morettin <pam@ime.usp.br>]

Seminário 

Séries Temporais, Análise de Dependência e Aplicações
em Atuaria e Finanças

Dia 17/10/06, 17:30h, Sala 247, Bloco A, Ime-Usp


"Probabilistic Treatment of a Reaction-diffusion Equation"


            Jose A. Lopez-Mimbela
        Centro de Investigacion en Matematicas
            Guanajuato, Mexico


Abstract: Reaction-diffusion equations are partial differential equations that
frequently arise as mathematical models in biology, physics and engineering.
In this talk we consider the Fujita equation, in which the diffusion
operator is the Laplacian and the reaction term is of power type.
It turns out that the qualitative behaviour of the Fujita equation is higly
dimensional-dependent,in the sense that there exists a critical dimension
below which any non-trivial positive solution exhibit finite-time blowup.
We shall give a probabilistic representation of solutions based on
multiplicative functionals of a pure birth process. Using such
representation, we shall explain intuitively when finite-time blowup occurs.



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Pedro Morettin <pam@ime.usp.br>