71 citations · 460 across the 61 of their papers we have counts for
8 papers · 2 filters
Existence and non-existence for the collision-induced breakage equation
Ankik Kumar Giri, Philippe Laurençot
A mathematical model for collision-induced breakage is considered. Existence of weak solutions to the continuous nonlinear collision-induced breakage equation is shown for a large…
Convergence of energy minimizers of a MEMS model in the reinforced limit
Philippe Laurençot, Katerina Nik, Christoph Walker
Energy minimizers to a MEMS model with an insulating layer are shown to converge in its reinforced limit to the minimizer of the limiting model as the thickness of the layer tends…
Sharp Sobolev estimates for concentration of solutions to an aggregation-diffusion equation
Piotr Biler, Alexandre Boritchev, Grzegorz Karch +1
We consider the drift-diffusion equation in the whole space with global-in-time solutions bounded in all Sobolev spaces; for simplicity, we…
Mass threshold for infinite-time blowup in a chemotaxis model with splitted population
Philippe Laurençot, Christian Stinner
We study the chemotaxis model t u = div(u -- uw) + v -- u in (0, ) x , t v = u -- v in (0, ) x , t w =…
Delayed Blow-Up for Chemotaxis Models with Local Sensing
Martin Burger, Philippe Laurençot, Ariane Trescases
The aim of this paper is to analyze a model for chemotaxis based on a local sensing mechanism instead of the gradient sensing mechanism used in the celebrated minimal Keller-Segel…
Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties
Philippe Laurençot, Katerina Nik, Christoph Walker
A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the in…
Stationary solutions to a nonlocal fourth-order elliptic obstacle problem
Philippe Laurençot, Christoph Walker
Existence of stationary solutions to a nonlocal fourth-order elliptic obstacle problem arising from the modelling of microelectromechanical systems with heterogeneous dielectric pr…
Concentration phenomena in a diffusive aggregation model
Piotr Biler, Alexandre Boritchev, Grzegorz Karch +1
We consider the drift-diffusion equation in the whole space with global-in-time bounded solutions. Mass concentration pheno…