14 papers · 1 filter
Strong gradient absorption and initial decay prevent blow-up
Philippe Souplet, Berikbol T. Torebek
Consider positive classical solutions of the Cauchy problem for , with sufficiently smooth initial data , in the strong absorption regime, namely $q\…
Sharp gradient bounds for uniformly elliptic PDE, eigenvalue asymptotics, and the Landis conjecture
Boyan Sirakov, Philippe Souplet
We study three classical problems in the theory of linear second-order uniformly elliptic equations: (i) gradient estimates for the Dirichlet problem, (ii) estimates and asymptotic…
Differential Harnack inequalities and maximum principles of Morel-Oswald type for elliptic PDE in divergence form
Philippe Souplet, Boyan Sirakov
This paper presents two types of novel, qualitative and quantitative, estimates for positive solutions of general uniformly elliptic PDEs in divergence form. First, we prove a More…
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 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…
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…
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…
Global existence and asymptotic behavior for diffusive Hamilton-Jacobi equations with Neumann boundary conditions
Joaquin Dominguez-de-Tena, Philippe Souplet
We investigate the diffusive Hamilton-Jacobi equation $$u_t-\Lap u = |\nabla u|^p$$ with , in a smooth bounded domain of $\RN$ with homogeneous Neumann boundary conditions and…
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…
Refined behavior and structural universality of the blow-up profile for the semilinear heat equation with non scale invariant nonlinearity
Loth Damagui Chabi, Philippe Souplet
We consider the semilinear heat equation for a large class of non scale invariant nonlinearities of the form , where is Sobolev subcritical and…
From transient elastic linkages to friction: a complete study of a penalized fourth order equation with delay
Vuk Milisic, Philippe Souplet
In this paper we consider a fourth order nonlinear parabolic delayed problem modelling a quasi-instantaneous turn-over of linkages in the context of cell-motility. The model depend…
Convergence, concentration and critical mass phenomena in a model of cell motion with boundary signal production
Nicolas Meunier, Philippe Souplet
We consider a model of cell motion with boundary signal production which describes some aspects of eukaryotic cell migration. Generic polarity markers located in the cell are trans…
Complete classification of gradient blow-up and recovery of boundary condition for the viscous Hamilton-Jacobi equation
Noriko Mizoguchi, Philippe Souplet
We study the Cauchy-Dirichlet pbm for superquadratic viscous Hamilton-Jacobi eq. We give a complete classification, namely rates and space-time profiles, in 1d case when viscosity…