Peter Takác

Ginzburg-Landau dynamics with a time-dependent magnetic field

The time-dependent Ginzburg-Landau equations of superconductivity define a dynamical process when the applied magnetic field varies with time. Sufficient conditions (in terms of the time rate of change of the applied field) are given that, if satisfied, guarantee that this dynamical process is asymptotically autonomous. As time goes to infinity, the dynamical process asymptotically approaches a dynamical system whose attractor coincides with the omega-limit set of the dynamical process.

Generalized minimizer solutions for equations with the

Let

p

varOmega

-Laplacian and a potential term

be a domain in

A Nonstiff Euler Discretization of the Complex Ginzburg--Landau Equation in One Space Dimension

mathbb{R}^N

Eigenfunctions and Hardy inequalities for a magnetic Schrödinger operator in ℝ2

(possibly unbounded),

An Extension of Maximum and Anti-Maximum Principles to a Schrödinger Equation in R2

Ngeq2

On the Number and Structure of Solutions for a Fredholm Alternative with the p-Laplacian

,

Bounded perturbations of homogeneous quasilinear operators using bifurcations from infinity

1 , and let

An equivalence relation for the Ginzburg-Landau equations of superconductivity

Vin L_{mathrm{loc}}^infty(varOmega)