Venue: Lecture Hall, 4th floor, Sir Run Run Shaw Business Administration Building
Speaker: Irene M. Gamba, Professor in Mathematics, W.A. Tex Moncreif, Jr. Chair in Computational Engineering and Sciences III. Leader for the ICES Applied Mathematics Group, the University of Texas at Austin
We look into the Cauchy problem for Homogeneous Boltzmann problems without initial bounded entropy and solve by means of theorem for ODE systems in Banach spaces. The technique works for collision frequencies satisfy that the larger the relative momentum the higher rate of interactions (i.e. hard potential) types with integrable angular cross section, and initial data the allows for a lower bound on the total collision frequency.This functional analysis, initially proposed for the Boltzmann equation, provides for a good tool works for a large variety of models, namely, the Cauchy problem for the classical elastic Boltzmann monoatomic gas model for hard potential and integrable angular cross sections, as well as for the multi-component monatomic gas mixture model in a full non-linear binary interactions. In addition, we used it for the quantum Boltzmann equation for a system with a BEC condensation, and the wave turbulence model proposed by Luov, Newell and Zacharov'95.