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Unique continuation for a quasilinear elliptic equation in the plane
Dead core Harnack inequality maximum principle nodal domain p-Laplacian p-harmonic quasilinear elliptic equation
2012/6/27
We consider planar solutions to certain quasilinear elliptic equations subject to the Dirichlet boundary conditions. We show that if the boundary data has finite number of relative maxima and minima t...
Nonlinear-damping continuation of the nonlinear Schrodinger equation - a numerical study
Nonlinear-damping continuation nonlinear Schrodinger equation Analysis of PDEs
2011/9/13
Abstract: We study the nonlinear-damping continuation of singular solutions of the critical and supercritical NLS. Our simulations suggest that for generic initial conditions that lead to collapse in ...
Unique continuation and approximate controllability for a degenerate parabolic equation
degenerate parabolic equations unique continuation approximate controllability local Carleman estimate
2011/9/13
Abstract: This paper studies unique continuation for weakly degenerate parabolic equations in one space dimension. A new Carleman estimate of local type is obtained to deduce that all solutions that v...
Numerical Continuation of resonances and bound states in coupled channel Schrödinger equations
Resonances Numerical Continuation Coupled Channels Schr¨odinger equation
2011/1/17
In this contribution, we introduce numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems,to the problem of tracing the parameter de...