Asymptotic analysis of mean exit time for dynamical systems with asingle well potential

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017077" target="_blank" >RIV/62690094:18470/20:50017077 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022039620302229/pdfft?md5=998bcec5efc4f4e26eb8f35724fd7749&pid=1-s2.0-S0022039620302229-main.pdf" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039620302229/pdfft?md5=998bcec5efc4f4e26eb8f35724fd7749&pid=1-s2.0-S0022039620302229-main.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2020.04.045" target="_blank" >10.1016/j.jde.2020.04.045</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Asymptotic analysis of mean exit time for dynamical systems with asingle well potential

Popis výsledku v původním jazyce

We study the mean exit time from a bounded multi-dimensional domain Omega of the stochastic process governed by the overdamped Langevin dynamics. This mean exit time solves the boundary value problem (-epsilon(2)Delta + del V . del)u(epsilon) = 1 in Omega, u(epsilon) = 0 on partial derivative Omega, epsilon -&gt; 0. The function Vis smooth enough and has the only minimum at the origin contained in Omega; the minimum can be degenerate. At other points of Omega, the gradient of Vis non-zero and the normal derivative of Vat the boundary partial derivative Omega does not vanish. Our main result is a complete asymptotic expansion for u(epsilon). The asymptotics for u(epsilon) involves an exponentially large term, which we find in a closed form. We also construct a power in epsilon asymptotic expansion such that this expansion and a mentioned exponentially large term approximate u(epsilon) up to arbitrary power of epsilon. (C) 2020 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Asymptotic analysis of mean exit time for dynamical systems with asingle well potential

Popis výsledku anglicky

We study the mean exit time from a bounded multi-dimensional domain Omega of the stochastic process governed by the overdamped Langevin dynamics. This mean exit time solves the boundary value problem (-epsilon(2)Delta + del V . del)u(epsilon) = 1 in Omega, u(epsilon) = 0 on partial derivative Omega, epsilon -&gt; 0. The function Vis smooth enough and has the only minimum at the origin contained in Omega; the minimum can be degenerate. At other points of Omega, the gradient of Vis non-zero and the normal derivative of Vat the boundary partial derivative Omega does not vanish. Our main result is a complete asymptotic expansion for u(epsilon). The asymptotics for u(epsilon) involves an exponentially large term, which we find in a closed form. We also construct a power in epsilon asymptotic expansion such that this expansion and a mentioned exponentially large term approximate u(epsilon) up to arbitrary power of epsilon. (C) 2020 Elsevier Inc. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of differential equations

ISSN

0022-0396

e-ISSN

—

Svazek periodika

269

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

39

Strana od-do

78-116

Kód UT WoS článku

000538395600004

EID výsledku v databázi Scopus

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