Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Dynamics and Differential Equations
ISSN
1040-7294
e-ISSN
1572-9222
Volume of the periodical
37
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
39
Pages from-to
687-725
UT code for WoS article
001011257600002
EID of the result in the Scopus database
2-s2.0-85161847595