Landau–Ginzburg-type equations on the half-line in the critical case

Abstract

We study nonlinear Landau-Ginzburg-type equations on the half-line in the critical casewhere β ∈ C, ρ > 2. The linear operator K is a pseudodifferential operator defined by the inverse Laplace transform with dissipative symbol K(p) = αp ρ , M = [ 1 2 ρ]. The aim of this paper is to prove the global existence of solutions to the initial-boundary-value problem and to find the main term of the asymptotic representation of solutions in the critical case, when the time decay of the nonlinearity has the same rate as that of the linear part of the equation.

Stochastic Landau–Ginzburg equation with white-noise boundary conditions of Robin type

“…There are relatively few papers discussing the non-homogeneous IBVP. Some of them are [7,12,[16][17][18][19] and [14]. The paper [8] is early work dealing with the dynamics of the CLG equation with deterministic inhomogeneous boundary data.…”