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14 papers · 2 filters
Asymptotic analysis of parabolic equations with stiff transport terms by a multi-scale approach
Thomas Blanc, Mihai Bostan, Franck Boyer
We perform the asymptotic analysis of parabolic equations with stiff transport terms. This kind of problem occurs, for example, in collisional gyrokinetic theory for tokamak plasma…
Discrete Artificial Boundary Conditions for the Korteweg-de Vries Equation
Christophe Besse, Matthias Ehrhardt, Ingrid Lacroix-Violet
In this paper we consider two numerical scheme based on trapezoidal rule in time for the linearized KdV equation in one space dimension. The goal is to derive some suitable artific…
Instantaneous shrinking and single point extinction for viscous Hamilton-Jacobi equations with fast diffusion
Razvan Gabriel Iagar, Philippe Laurençot, Christian Stinner
For a large class of non-negative initial data, the solutions to the quasilinear viscous Hamilton-Jacobi equation in …
Sharp reversed Hardy--Littlewood--Sobolev inequality on the half space
Quôc-Anh Ngô, Van Hoang Nguyen
This is the second in our series of papers concerning some reversed Hardy--Littlewood--Sobolev inequalities. In the present work, we establish the following sharp reversed Hardy--L…
On the Cauchy problem and the black solitons of a singularly perturbed Gross-Pitaevskii equation
Isabella Ianni, Stefan Le Coz, Julien Royer
We consider the one-dimensional Gross-Pitaevskii equation perturbed by a Dirac potential. Using a fine analysis of the properties of the linear propagator, we study the well-posedn…
On a three-dimensional free boundary problem modeling electrostatic mems
Philippe Laurencot, Christoph Walker
We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. The model includes the harmonic electrostatic potent…