4 papers
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…
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…