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Activity Number: 105
Type: Contributed
Date/Time: Monday, August 4, 2008 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #301823
Title: Nonexplosion of a Class of Semilinear Partial Differential Equations via Branching Particle Representations
Author(s): Santanu Chakraborty*+ and Jose A. Lopez Mimbela
Companies: University of Texas - Pan American and Centro de Investigacion en Matematicas
Address: 1201 West University Drive, Edinburg, TX, 78541,
Keywords: Branching particle systems ; Semilinear partial differential equations ; Global positive solutions
Abstract:

We consider a branching particle system where an individual particle gives birth to a random number of offspring at the place where it dies before its death. We assume a discrete probability distribution on the number of offspring. The corresponding branching process is described by a semilinear partial differential equation. We obtain sufficient conditions for existence of global positive solutions to semilinear equations of this form. These conditions answer questions regarding a population becoming extinct in future.

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Revised September, 2008