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 2014Show all

3 papers · 1 filter

math.AP2014★ 1 cited

A priori estimates and bifurcation of solutions for a noncoercive elliptic equation with critical growth in the gradient

Philippe Souplet

We study nonnegative solutions of the boundary value problem $$-Δu = λc(x)u + μ(x)|\nabla u|^2 + h(x),\quad u\in H^1_0(Ω)\cap L^\infty(Ω), \leqno(P_λ)$$ where $Ω$ is a smooth bound…

math.AP2014

No touchdown at zero points of the permittivity profile for the MEMS problem

Jong-Shenq Guo, Phlippe Souplet

We study the quenching behavior for a semilinear heat equation arising in models of micro-electro mechanical systems (MEMS). The problem involves a source term with a spatially dep…

math.AP2014

Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with $p$ -Laplacian diffusion

Amal Attouchi, Philippe Souplet

We study the initial-boundary value problem for the Hamilton-Jacobi equation with nonlinear diffusion $u_{t} = Δ_{p} u + ∣\nabla u ∣^{q}$ in a two-dimensional domain for $q > p > 2$ . It is known…

A priori estimates and bifurcation of solutions for a noncoercive elliptic equation with critical growth in the gradient

No touchdown at zero points of the permittivity profile for the MEMS problem

Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with p-Laplacian diffusion

Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with $p$ -Laplacian diffusion