Shuichi Jimbo

The singularly perturbed domain and the characterization for the eigenfunctions with Neumann boundary condition

On considere un domaine mobile Ω(ξ)|(ξ>0:|parametre) qui degenere partiellement quand ξ→0 et on donne une caracterisation elaboree des comportements des fonctions propres du laplacien avec la condition limite de Neumann

Ginzburg-Landau equations and stable solutions in a rotational domain

The Ginzburg–Landau (GL) equations, with or without magnetic effect, are studied in the case of a rotational domain in

Ginzburg-Landau equation and stable steady state solutions in a non-trivial domain

\mathbb{R}^3

Singular perturbation of domains and the semilinear elliptic equation, II

. It can be shown that there exist rotational solutions which describe the physical state of permanent current of electrons in a ring-shaped superconductor. Moreover, if a physical parameter—called the GL parameter—is sufficiently large, then these solutions are stable, that is, they are local minimizers of an energy functional (GL energy). This is proved by the spectral analysis on the linearized equation.

Stabilization of vortices in the Ginzburg-Landau equation with a variable diffusion coefficient

The Ginzburg-Landau equation with a large parameter is studied in a bounded domain with the Neumann B.C. It is shown that many kinds of stable non-constant solutions exist in domains with some topological condition. If the space dimension is 2 or 3 and if the domain is not simply connected, this condition holds. 25 refs.

NONEXISTENCE OF PERMANENT CURRENTS IN CONVEX PLANAR SAMPLES

On considere un domaine a perturbation singuliere Ω(ζ)=D 1 ∪D 2 ∪Q(ζ) avec un petit parametre ζ>0 et on etudie le comportement des solutions et leur structure du probleme aux valeurs limites elliptique semilineaire pour Ω=Ω(ζ) quand ζ>0 est petit: Δv+f(v)=0 dans Ω, ∂v/∂v=0 sur ∂Ω; ou f est une fonction lisse a valeur reelle non lineaire

A non-destructive method for damage detection in steel-concrete structures based on finite eigendata

We study equilibria of the Ginzburg--Landau equation with a variable diffusion coefficient on a bounded planar domain subject to the Neumann boundary condition. It has been previously shown that if the diffusion coefficient is constant and the ambient domain is convex, the system does not carry stable vortices in the sense that any stable equilibrium solution is a constant of modulus 1. In this article we shall prove that arbitrarily given a domain, an appropriate choice of inhomogeneous diffusion coefficient yields a stable equilibrium solution having vortices. We can even manage to make the configuration of stable vortices close to prescribed locations. Our method is to minimize the free energy functional in suitably constructed positive invariant regions for the time-dependent Ginzburg--Landau equation.

Spectral comparison and gradient-like property in the FitzHugh–Nagumo type equations

Recent works have demonstrated the existence of nontrivial stable critical points of the Ginzburg--Landau energy

Approximation of Eigenvalues of Elliptic Operators with Discontinuous Coefficients

(\Psi,A)\to\int_{\Omega} \frac{1}{2}|(\nabla-iA)\Psi|^{2}+\frac{\kappa^{2} }{4} (...