Type: Article

Nonlinear model of quasi-stationary process in crystalline semiconductor

Juárez Campos, B; Kaikina, Elena; Paredes Ruiz, Héctor F.;

Abstract:

We consider the question of global existence and asymptotics of small, smooth, and localized solutions of a certain pseudoparabolic equation in one dimension, posed on half-line x > 0, { (1 -partial derivative(2)(x)) u(t) =partial derivative(2)(x) (u + alpha(2) (|u|(q2) u)) + alpha(1) |u|(q1) u, x epsilon R+, t > 0, u(0,x) = u(0) (x), x epsilon R+, u(0,t) = h(t), (0.1) where alpha(i) epsilon R, q(i) > 0, i = 1,2,u : R-x(+) x R-t(+) epsilon C. This model is motivated by the a wave equation for media with a strong spatial dispersion, which appear in the nonlinear theory of the quasy-stationary processes in the electric media. We show that the problem (0.1) admits global solutions whose long-time behavior depend on boundary data. More precisely, we prove global existence and modified by boundary scattering of solutions.