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27 papers · 1 filter
Global Lipschitz continuity for minima of degenerate problems
Pierre Bousquet, Lorenzo Brasco
We consider the problem of minimizing the Lagrangian among functions on with given boundary datum . We prove Lipschitz regularit…
Large time behavior for a quasilinear diffusion equation with critical gradient absorption
Razvan Gabriel Iagar, Philippe Laurençot
We study the large time behavior of non-negative solutions to the nonlinear diffusion equation with critical gradient absorption $$\partial\_t u - Δ\_{p}u + |\nabla u|^{q\_*} = 0 \…
Existence of travelling waves for a reaction-diffusion system with a line of fast diffusion
Laurent Dietrich
We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a lin…
Large time behavior for the fast diffusion equation with critical absorption
Said Benachour, Razvan Gabriel Iagar, Philippe Laurencot
We study the large time behavior of nonnegative solutions to the Cauchy problem for a fast diffusion equation with critical zero order absorption $$ \partial_{t}u-Δu^m+u^q=0 \quad…
A model of individual clustering with vanishing diffusion
Elissar Nasreddine
We consider a model of individual clustering with two specific reproduction rates and small diffusion parameter in one space dimension. It consists of a drift-diffusion equation fo…
A parabolic free boundary problem modeling electrostatic MEMS
Joachim Escher, Philippe Laurencot, Christoph Walker
The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system (MEMS) is studied. The model describes the dynamics of the membrane…