Self-similar behaviour of a non-local diffusion equation with time delay
GENADOT, Alexandre
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
GENADOT, Alexandre
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Document de travail - Pré-publication
English Abstract
We study the asymptotic behaviour of solutions of a class of linear non-local measure-valued differential equations with time delay. Our main result states that the solutions asymptotically exhibit a parabolic like behaviour ...Read more >
We study the asymptotic behaviour of solutions of a class of linear non-local measure-valued differential equations with time delay. Our main result states that the solutions asymptotically exhibit a parabolic like behaviour in the large times, that is precisely expressed in term of heat kernel. Our proof relies on the study of a-self-similar-rescaled family of solutions. We first identify the asymptotic behaviour of the solutions by deriving a convergence result in the sense of the Young measures. Then we strengthen this convergence by deriving suitable fractional Sobolev compactness estimates. As a by-product, our main result allows to obtain asymptotic results for a class of piecewise constant stochastic processes with memory.Read less <
English Keywords
Non-local diffusion
Time delay
Self-similar behaviour
Fractional Sobolev estimates
Central Limit Theorem
Origin
Hal imported