P. Souplet

activity

20052026

most citedBlow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions

n \geq 3

61 citations · 170 across the 25 of their papers we have counts for

collaborators

Showing 2019Show all

4 papers · 1 filter

math.AP2019★ 11 cited

Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations

Amal Attouchi, Philippe Souplet

Consider the diffusive Hamilton-Jacobi equation $u_{t} - Δ u = ∣\nabla u ∣^{p} + h (x) in Ω \times (0, T)$ with Dirichlet conditions, which arises in stochastic control problems as w…

math.AP2019

A Liouville-type theorem for an elliptic equation with superquadratic growth in the gradient

Roberta Filippucci, Patrizia Pucci, Philippe Souplet

We consider the elliptic equation $- Δ u = u^{q} ∣\nabla u ∣^{p}$ in $R^{n}$ for any $p \geq 2$ and $q > 0$ . We prove a Liouville-type theorem, which asserts that any positive bounded so…

math.AP2019

Discontinuous critical Fujita exponents for the heat equation with combined nonlinearities

Mohamed Jleli, Bessem Samet, Philippe Souplet

We consider the nonlinear heat equation $u_{t} - Δ u = ∣ u ∣^{p} + b ∣\nabla u ∣^{q}$ in $(0, \infty) \times R^{n}$ , where $n \geq 1$ , $p > 1$ , $q \geq 1$ and $b > 0$ . First, we focus our attention on pos…

math.AP2019

A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton-Jacobi equations

Roberta Filippucci, Patrizia Pucci, Philippe Souplet

We consider the elliptic and parabolic superquadratic diffusive Hamilton-Jacobi equations with homogeneous Dirichlet conditions. For the elliptic problem in a half-space, we prove…