Initial-boundary value problems for nonlinear pseudoparabolic equations in a critical case

Abstract

We study nonlinear pseudoparabolic equations, on the half-line in a critical case, ∂t(u - uₓₓ) - αuₓₓ = λ|u|u, x ∈ ℝ⁺, t > 0, u(0, x) = u0(x), x ∈ ℝ⁺, u(t, 0) = 0, where α > 0, λ ∈ ℝ. The aim of this paper is to prove the existence of global solutions to the initial-boundary value problem and to find the main term of the asymptotic representation of solutions.