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Displaying similar documents to “Uniform estimates for the parabolic Ginzburg–Landau equation”

Morse index and blow-up points of solutions of some nonlinear problems

Khalil El Mehdi, Filomena Pacella (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this Note we consider the following problem - u = N N - 2 u p ϵ - λ u in  Ω u > 0 in  Ω u = 0 on  Ω . where Ω is a bounded smooth starshaped domain in R N , N 3 , p ϵ = N + 2 N - 2 - ϵ , ϵ > 0 , and λ 0 . We prove that if u ϵ is a solution of Morse index m > 0 than u ϵ cannot have more than m maximum points in Ω for ϵ sufficiently small. Moreover if Ω is convex we prove that any solution of index one has only one critical point and the level sets are starshaped for ϵ sufficiently small.

Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics

F. Bethuel, G. Orlandi, D. Smets (2004)

Journées Équations aux dérivées partielles

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We discuss the asymptotics of the parabolic Ginzburg-Landau equation in dimension N 2 . Our only asumption on the initial datum is a natural energy bound. Compared to the case of “well-prepared” initial datum, this induces possible new energy modes which we analyze, and in particular their mutual interaction. The two dimensional case is qualitatively different and requires a separate treatment.

Homogenization and localization in locally periodic transport

Grégoire Allaire, Guillaume Bal, Vincent Siess (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we study the homogenization and localization of a spectral transport equation posed in a locally periodic heterogeneous domain. This equation models the equilibrium of particles interacting with an underlying medium in the presence of a creation mechanism such as, for instance, neutrons in nuclear reactors. The physical coefficients of the domain are ε -periodic functions modulated by a macroscopic variable, where ε is a small parameter. The mean free path of the particles...

Limiting behavior of global attractors for singularly perturbed beam equations with strong damping

Daniel Ševčovič (1991)

Commentationes Mathematicae Universitatis Carolinae

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The limiting behavior of global attractors 𝒜 ε for singularly perturbed beam equations ε 2 2 u t 2 + ε δ u t + A u t + α A u + g ( u 1 / 4 2 ) A 1 / 2 u = 0 is investigated. It is shown that for any neighborhood 𝒰 of 𝒜 0 the set 𝒜 ε is included in 𝒰 for ε small.