61 citations · 170 across the 25 of their papers we have counts for
4 papers · 2 filters
Optimal condition for blow-up of the critical norm for the semilinear heat equation
Noriko Mizoguchi, Philippe Souplet
We shed light on a long-standing open question for the semilinear heat equation . Namely, without any restriction on the exponent nor on the smooth do…
Blow-up and regularization rates, loss and recovery of boundary conditions for the superquadratic viscous Hamilton-Jacobi equation
Alessio Porretta, Philippe Souplet
We study the qualitative properties of the unique global viscosity solution of the superquadratic diffusive Hamilton-Jacobi equation with (generalized) homogeneous Dirichlet condit…
Global existence for reaction-diffusion systems with dissipation of mass and quadratic growth
Philippe Souplet
We consider the Neumann and Cauchy problems for positivity preserving reaction-diffusion systems of equations enjoying the mass and entropy dissipation properties. We show glob…
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions
Philippe Souplet, Michael Winkler
We study the blow-up asymptotics of radially decreasing solutions of the parabolic-elliptic Keller-Segel-Patlak system in space dimensions . In view of the biological backg…