10 papers
Blow-up for weakly superlinear heat equations and blow-up controllability of the linear heat equation
Kévin Le Balc'h, Philippe Souplet
The aim of this article is twofold: (a) to revisit the blow-up theory of weakly superlinear heat equations; (b) to explore the notion of internal global/regional blow-up controllab…
Sharp macroscopic blow-up behavior for the parabolic-elliptic Keller-Segel system in dimensions
Loth Damagui Chabi, Philippe Souplet
We study the space-time concentration or blow-up asymptotics of radially decreasing solutions of the parabolic-elliptic Keller-Segel system in the whole space or in a ball. We show…
Classification of entire and ancient solutions of the diffusive Hamilton-Jacobi equation
Loth Damagui Chabi, Philippe Souplet
Consider the diffusive HJ eq. with Dirichlet conditions, which arises in stochastic control as well as in KPZ type models of surface growth. It is known that, for and suitabl…
Classification of solutions of an elliptic Hamilton-Jacobi equation
Alessio Porretta, Philippe Souplet
We show that any classical solution of the diffusive Hamilton-Jacobi (DHJ) equation in a half-space with zero boundary conditions for is necessarily…
Optimal Hamilton-type gradient estimates and large time heat kernel bounds for noncompact manifolds
Loth Damagui Chabi, Philippe Souplet
We derive localized and global noncompact versions of Ham\-ilton's gradient estimate for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounde…
A Liouville theorem for the Lane-Emden system in the half-space
Yimei Li, Philippe Souplet
We prove that the Dirichlet problem for the Lane-Emden system in a half-space has no positive classical solution that is bounded on finite strips. Such a nonexistence result was pr…