6th session, October 6th & 7th 2014
Monday 6th ReaDi-EHESS, 190-198 av. de France, 75013 Paris, Room 466
14h - 15h : Luca Rossi
Valeur propre principale généralisée dans des cadres non compacts
On se pose la question de trouver un analogue de la valeur propre principale pour des opérateurs dont la résolvante n'est pas compacte. On considère d'abord le cas ou la non compacité est due au fait que le domaine est non borne, ou on montre qu'on a besoin de plusieurs notions pour caractériser les propriétés de la valeur propre principale concernant l'existence de fonctions propres positives et le principe du maximum. Ensuite, on traitera le cas des opérateurs dégénérés dans le cadre des solutions de viscosité.
On se pose la question de trouver un analogue de la valeur propre principale pour des opérateurs dont la résolvante n'est pas compacte. On considère d'abord le cas ou la non compacité est due au fait que le domaine est non borne, ou on montre qu'on a besoin de plusieurs notions pour caractériser les propriétés de la valeur propre principale concernant l'existence de fonctions propres positives et le principe du maximum. Ensuite, on traitera le cas des opérateurs dégénérés dans le cadre des solutions de viscosité.
15h15 - 16h15 : Jian Fang
On the propagation direction of bistable waves in a nonlocal reaction-diffusion equation
In this paper, we observe that varying the rate of symmetric non-local interaction in a reaction-diffusion equation may alter the propagation direction of bistable traveling waves. To ensure such a phenomena happens or not happen, we give some sufficient explicit conditions.
In this paper, we observe that varying the rate of symmetric non-local interaction in a reaction-diffusion equation may alter the propagation direction of bistable traveling waves. To ensure such a phenomena happens or not happen, we give some sufficient explicit conditions.
16h15 - 16h45 : Coffee
16h45 - 17h45 : Andrea Tellini
Tuesday 7th ReaDi-EHESS, 190-198 av. de France, 75013 Paris, Room 466
9h15 - 9h45 : Coffee
9h45 - 10h45 : Grégory Faye
A dynamical systems approach to some nonlocal problems
In this talk, we will present some recent results on nonlocal problems using ideas from dynamical systems theory. In a first part, we will study propagation failure in nonlocal Allen-Cahn equations and present results on unpinning asymptotics for the wave speed (as one approaches the pinning region) using singular perturbations theory. In a second part, we analyze the existence of traveling pulses for the Fitz-Hugh Nagumo equations when the diffusion is nonlocal. Here, the proof relies on matched asymptotics techniques and Fredholm properties of differential operators on suitable Banach spaces. Finally, if times allows, we will study the existence of periodic states and modulated traveling waves in the nonlocal Fisher-KPP using center manifold techniques.
In this talk, we will present some recent results on nonlocal problems using ideas from dynamical systems theory. In a first part, we will study propagation failure in nonlocal Allen-Cahn equations and present results on unpinning asymptotics for the wave speed (as one approaches the pinning region) using singular perturbations theory. In a second part, we analyze the existence of traveling pulses for the Fitz-Hugh Nagumo equations when the diffusion is nonlocal. Here, the proof relies on matched asymptotics techniques and Fredholm properties of differential operators on suitable Banach spaces. Finally, if times allows, we will study the existence of periodic states and modulated traveling waves in the nonlocal Fisher-KPP using center manifold techniques.
11h - 12h : Alessandro Zilio
14h - 15h : Luca Rossi
Suite de l'exposé