71 citations · 460 across the 61 of their papers we have counts for
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Sharp non-existence threshold for a parabolic Hardy-H{é}non equation with quasilinear diffusion
Razvan Gabriel Iagar, Philippe Laurençot
Optimal conditions for initial data leading to non-existence of non-negative solutions to the Cauchy problem for the parabolic Hardy-H{é}non equation $$ \partial\_tu=Δu^m+|x|^σu^p,…
Global bounded classical solutions to a parabolic-elliptic chemotaxis model with local sensing and asymptotically unbounded motility
Jie Jiang, Philippe Laurençot
Global existence and boundedness of classical solutions are shown for a parabolic-elliptic chemotaxis system with local sensing when the motility function is assumed to be unbounde…
Stationary states to a free boundary transmission problem for an electrostatically actuated plate
Philippe Laurençot, Christoph Walker
A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of…
Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption
Jie Jiang, Philippe Laurençot, Yanyan Zhang
Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics of a population of cells…
The fragmentation equation with size diffusion: Well-posedness and long-term behavior
Philippe Laurençot, Christoph Walker
The dynamics of the fragmentation equation with size diffusion is investigated when the size ranges in (0, ). The associated linear operator involves three terms and can be…
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…
Reinforced limit of a MEMS model with heterogeneous dielectric properties
Philippe Laurençot, Katerina Nik, Christoph Walker
A MEMS model with an insulating layer is considered and its reinforced limit is derived by means of a Gamma convergence approach when the thickness of the layer tends to zero. The…
Mass-conserving self-similar solutions to coagulation-fragmentation equations
Philippe Laurençot
Existence of mass-conserving self-similar solutions with a sufficiently small total mass is proved for a specific class of homogeneous coagulation and fragmentation coefficients. T…
Shape derivative of the Dirichlet energy for a transmission problem
Philippe Laurençot, Christoph Walker
For a transmission problem in a truncated two-dimensional cylinder located beneath the graph of a function u, the shape derivative of the Dirichlet energy (with respect to u) is sh…
Mass-conserving solutions to the Smoluchowski coagulation equation with singular kernel
Prasanta Kumar Barik, Ankik Kumar Giri, Philippe Laurençot
Global weak solutions to the continuous Smoluchowski coagulation equation (SCE) are constructed for coagulation kernels featuring an algebraic singularity for small volumes and gro…
Extinction for a singular diffusion equation with strong gradient absorption revisited
Razvan Iagar, Philippe Laurençot
When and , non-negative solutions to the singular diffusion equation with gradient absorption $$\partial\_tu-Δ\_p u + |\nabla u|^q=0 \ \text{ in }\ (0,\inft…
Optimal extinction rates for the fast diffusion equation with strong absorption
Razvan Iagar, Philippe Laurençot
Optimal extinction rates near the extinction time are derived for non-negative solutions to a fast diffusion equation with strong absorption, the power of the absorption exceeding…
A constrained model for MEMS with varying dielectric properties
Philippe Laurencot, Christoph Walker
A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-kn…
Heterogeneous dielectric properties in MEMS models
Philippe Laurencot, Christoph Walker
An idealized electrostatically actuated microelectromechanical system (MEMS) involving an elastic plate with a heterogeneous dielectric material is considered. Starting from the el…
Some singular equations modeling MEMS
Philippe Laurencot, Christoph Walker
In the past fifteen years mathematical models for microelectromechanical systems (MEMS) have been the subject of several studies, in particular due to the interesting qualitative p…
Finite time singularity in a MEMS model revisited
Philippe Laurençot, Christoph Walker
A free boundary problem modeling a microelectromechanical system (MEMS) consisting of a fixed ground plate and a deformable top plate is considered, the plates being held at differ…
Self-similar extinction for a diffusive Hamilton-Jacobi equation with critical absorption
Razvan Gabriel Iagar, Philippe Laurençot
The behavior near the extinction time is identified for non-negative solutions to the diffusive Hamilton-Jacobi equation with critical gradient absorption $\partial_t u - Δ_p u + |…