Time

Jun 5 2007 - 2:30pm - 3:20 pm

Location

MW154

Speaker

Cecil Grunfeld (Institute of Space Sciences, Bucharest& Institute of Statistical Mathematics and Applied Mathematics of the Romanian Academy)

Abstract

The Cauchy problem for a nonlinear evolution equation is investigated, formulated in an abstract Lebesgue space, as a generalization of various Boltzmann kinetic models. Our main result provides sufficient conditions for the existence, uniqueness, and positivity of global in time solutions. The analysis extends nontrivially monotonicity methods, originally developed in the context of the existence theory for the classical Boltzmann equation in L1. Application examples are Smoluchowski's coagulation equation, a Povzner-like equation with dissipative collisions, and a Boltzmann model with chemical reactions, for which we obtain a unitary existence theory, with improved results, compared to the literature.