8 papers
Refined blow-up behavior for semilinear heat equations with arbitrarily fast growing nonlinearities
Loth Damagui Chabi
We study radially nonincreasing, positive blow-up solutions of a class of superlinear heat equations in the non-scale-invariant setting. This class contains nonlinearities with arb…
Local existence and blow-up behavior for the diffusive Hamilton-Jacobi equation in a half-space with unbounded initial data
Loth Damagui Chabi
We study the local existence and blow-up behavior of solutions, with possible growth at space infinity, for the diffusive Hamilton-Jacobi equation (), in…
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…
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…
Refined blow-up behavior for reaction-diffusion equations with non scale invariant exponential nonlinearities
Loth Damagui Chabi
We consider positive radial decreasing blow-up solutions of the semilinear heat equation \begin{equation*} u_t-Δu=f(u):=e^{u}L(e^{u}),\quad x\in Ω,\ t>0, \end{equation*} where $Ω=\…
Asymptotic blow-up behavior for the semilinear heat equation with non scale invariant nonlinearity
Loth Damagui Chabi
We characterize the asymptotic behavior near blowup points for positive solutions of the semilinear heat equation \begin{equation*} \partial_t u-Δu =f(u), \end{equation*} for nonli…
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…