41 citations · 41 across the 2 of their papers we have counts for
5 papers
Behavior of the free boundary near contact points with the fixed boundary for nonlinear elliptic equations
Norayr Matevosyan, Peter Markowich
The aim of this paper is to study a free boundary problem for a uniformly elliptic fully non-linear operator. Under certain assumptions we show that free and fixed boundaries meet…
Semiclassical asymptotics for weakly nonlinear Bloch waves
Remi Carles, Peter A. Markowich, Christof Sparber
We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schroedinger equations with a fast periodic potential and a slowly varying conf…
On the Long Time Behavior of the Quantum Fokker-Planck equation
C. Sparber, J. A. Carrillo, J. Dolbeault +1
We analyze the long time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type scattering operator, subject to confining potentials of…
Wigner Functions versus WKB-Methods in Multivalued Geometrical Optics
Christof Sparber, Peter A. Markowich, Norbert J. Mauser
We consider the Cauchy-problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of high-frequency asymptotics of such models is…
Existence and nonlinear stability of steady states of the Schrödinger-Poisson system
Peter A. Markowich, Gerhard Rein, Gershon Wolansky
We consider the Schrödinger-Poisson system in the attractive (plasma physics) Coulomb case. Given a steady state from a certain class we prove its nonlinear stability, using an app…