Global Solutions of Cauchy problem for Nonlinear Boltzmann and Smoluchowskii Equations

摘要

The paper is devoted to the background of correctness for systems of nonlinear equations possessing applied significance in mathematical physics particularly in gas and fluid dynamics (Euler equations), in physical kinetics (Boltzmann and Smoluchovskii equations) and in phase transition models. The nonlinear operators in above equations are not continuous in Banach spaces specific for these conservation laws. There are discussed general mathematical striictures, connected with approximate methods convergence. The existence and uniqueness theorems for global solutions of Cauchy problem for quasilinear and semilinear systems are proved. The problems of computations in above models are discussed too.