Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F25%3APU149859" target="_blank" >RIV/00216305:26220/25:PU149859 - isvavai.cz</a>

Výsledek na webu

<a href="https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001011257600002" target="_blank" >https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001011257600002</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10884-023-10278-y" target="_blank" >10.1007/s10884-023-10278-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions

Popis výsledku v původním jazyce

In this paper, we study the initial boundary value problem for the nonlocal parabolic equation with the Hardy-Littlewood-Sobolev critical exponent on a bounded domain. We are concerned with the long time behaviors of solutions when the initial energy is low, critical or high. More precisely, by using the modified potential well method, we obtain global existence and blow-up of solutions when the initial energy is low or critical, and it is proved that the global solutions are classical. Moreover, we obtain an upper bound of blow-up time for J(mu)(u0) < 0 and decay rate of H-0(1) and L-2-norm of the global solutions. When the initial energy is high, we derive some sufficient conditions for global existence and blow-up of solutions. In addition, we are going to consider the asymptotic behavior of global solutions, which is similar to the Palais-Smale (PS for short) sequence of stationary equation.

Název v anglickém jazyce

Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions

Popis výsledku anglicky

In this paper, we study the initial boundary value problem for the nonlocal parabolic equation with the Hardy-Littlewood-Sobolev critical exponent on a bounded domain. We are concerned with the long time behaviors of solutions when the initial energy is low, critical or high. More precisely, by using the modified potential well method, we obtain global existence and blow-up of solutions when the initial energy is low or critical, and it is proved that the global solutions are classical. Moreover, we obtain an upper bound of blow-up time for J(mu)(u0) < 0 and decay rate of H-0(1) and L-2-norm of the global solutions. When the initial energy is high, we derive some sufficient conditions for global existence and blow-up of solutions. In addition, we are going to consider the asymptotic behavior of global solutions, which is similar to the Palais-Smale (PS for short) sequence of stationary equation.

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

2025

Kód důvěrnosti údajů

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

Název periodika

Journal of Dynamics and Differential Equations

ISSN

1040-7294

e-ISSN

1572-9222

Svazek periodika

37

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

39

Strana od-do

687-725

Kód UT WoS článku

001011257600002

EID výsledku v databázi Scopus

2-s2.0-85161847595