Finite-time relaxation of the solution of a nonlinear pseudoparabolic equation

A model equation is considered that describes the relaxation of an initial perturbation in a crystalline semiconductor in the case when its electrical conductivity depends nonlocally on the field. For certain initial parameters, the effect of finite-time “cooling” is proved to occur. For other parameters, the first term of the long-time asymptotics is found and the remainder of the asymptotic expansion is estimated.