Factorization techniques for the nonlinear model of quasi-stationary processes in crystalline semiconductors

Abstract

We consider the question of global existence and asymptotics of small solutions of a certain pseudoparabolic equation in one dimension . This model is motivated by the wave equation for media with a strong spatial dispersion, which appear in the nonlinear theory of the quasi-stationary processes in the electric media. We develop the factorization technique to study the large time asymptotics of solutions.