BOUNDARY PROBLEMS FOR THE GINZBURG–LANDAU EQUATION

Boundary problems for the Ginzburg-Landau equation

We provide a study at the boundary for a class of equation including the Ginzburg-Landau equation as well as the equation of travelling waves for the Gross-Pitaevskii model. We prove Clearing-Out results and an orthogonal anchoring condition of the vortex on the boundary for the Ginzburg-Landau equation with magnetic field.

Integral Equation Methods for Free Boundary Problems∗

We outline a unified approach for treating free boundary problems arising in Finance using integral equation methods. Starting with the PDE formulations of the free boundary problems, we show how to derive nonlinear integral equations for the free boundaries in a variety of Finance applications. Methods to treat theoretical (existence, uniqueness) questions and analytical and numerical approxim...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Inverse Boundary Value Problems for the Magnetic Schrödinger Equation

We survey recent results on inverse boundary value problems for the magnetic Schrödinger equation.

Two Boundary Value Problems for the Ginzburg-landau Equation

Two boundary value problems for the Ginzburg-Landau equation are considered. Extensive numerical calculations have been performed in each case, including bifurcation histories, spectral analysis, PoincarC sections and Hausdorff dimension estimates. The approach to the inviscid limit is given detailed treatment. In this case universal behavior has been found to exist. Arguments are presented to ...