3 citations · 10 across the 9 of their papers we have counts for
10 papers
Sharp Decay Estimates and Vanishing Viscosity for Diffusive Hamilton-Jacobi Equations
Said Benachour, Matania Ben-Artzi, Philippe Laurençot
Sharp temporal decay estimates are established for the gradient and time derivative of solutions to a viscous Hamilton-Jacobi equation as well the associated Hamilton-Jacobi equati…
Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system
Tomasz Cieślak, Philippe Laurençot
Finite time blow-up is shown to occur for solutions to a one-dimensional quasilinear parabolic-parabolic chemotaxis system as soon as the mean value of the initial condition exceed…
Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system
Tomasz Cieślak, Philippe Laurençot
Finite time blow-up is shown to occur for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system provided that the mass of the initial condition exceeds…
Proteus mirabilis swarm-colony development with drift
Philippe Laurençot, Christoph Walker
We prove a global existence result for a model describing the swarming phenomenon of the bacterium Proteus mirabilis. The model consists of an ordinary differential equation couple…
Non-diffusive large time behaviour for a degenerate viscous Hamilton-Jacobi equation
Philippe Laurençot
The convergence to non-diffusive self-similar solutions is investigated for non-negative solutions to the Cauchy problem when the initial data…
Fermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics
José A. Carrillo, Philippe Laurençot, Jesús Rosado
A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of…