Daniel Phillips

The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model

We study the behavior of a superconducting material subjected to a constant applied magnetic field,

Stabilization of solutions of nonlinear and degenerate evolution equations

\bH_a=h\bee

The free boundary of a semilinear elliptic equation

with

A nonconvex variational problem related to change of phase

|\bee|=1

Maximum principles and a priori estimates for a class of problems from nonlinear elasticity

, using the Ginzburg--Landau theory. We analytically show the existence of a critical field

Analysis of Nematic Liquid Crystals with Disclination Lines

\oh,

On the zeros of solutions to Ginzburg-Landau type systems

for which when

Maximal smoothness of solutions to certain Euler-Lagrange equations from nonlinear elasticity

h>\oh,

Vortex annihilation in nonlinear heat flow for Ginzburg–Landau systems

the normal states are the only solutions to the Ginzburg--Landau equations. We estimate

On the analysis of a non-isothermal model for superconductivity

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