Landau–Ginzburg-type equations on the half-line in the critical case
Published online by Cambridge University Press: 12 July 2007
Abstract
We study nonlinear Landau–Ginzburg-type equations on the half-line in the critical case where β ∈ C, ρ > 2. The linear operator K is a pseudodifferential operator defined by the inverse Laplace transform with dissipative symbol K(p) = αpρ, M = [1/2ρ]. 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.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 6 , December 2005 , pp. 1241 - 1262
- Copyright
- Copyright © Royal Society of Edinburgh 2005
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