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9 papers · 2 filters
On the instability of threshold solutions of reaction-diffusion equations, and applications to optimization problems
Grégoire Nadin
The first part of this paper is devoted to the derivation of a technical result, related to the stability of the solution of a reaction-diffusion equation on $(0,…
An optimal spectral inequality for degenerate operators
Rémi Buffe, Kim Dang Phung, Amine Slimani
In this paper we establish a Lebeau-Robbiano spectral inequality for a degenerate one dimensional elliptic operator. Carleman techniques and moment method are combined. Application…
The Cauchy problem associated to the logarithmic Laplacian with an application to the fundamental solution
Huyuan Chen, Laurent Véron
Let $\lnlap$ be the logarithmic Laplacian operator with Fourier symbol , we study the expression of the diffusion kernel which is associated to the equation $$\partial_tu…
Upper bounds for the blow-up time of the 2-D parabolic-elliptic Patlak-Keller-Segel model of chemotaxis
Patrick Maheux
In this paper, we obtain upper bounds for the critical time of the blow-up for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. No moment conditio…
Modeling compartmentalization within intracellular signaling pathway
Claire Alamichel, Juan Calvo, Erwan Hingant +3
We present a new modeling approach for G protein coupled receptors signaling systems, that take into account the compartmentalization of receptors and their effectors, both at plas…
Long-time asymptotic of the Lifshitz-Slyozov equation with nucleation
Juan Calvo, Erwan Hingant, Romain Yvinec
We consider the Lifshitz-Slyozov model with inflow boundary conditions of nucleation type. We show that for a collection of representative rate functions the size distributions app…