Bounds for the blow-up time a class of integro-differential problem of parabolic type with variable reaction term

Rabil Ayazoglu; Ebubekir Akkoyunlu

doi:10.5802/crmeca.233

Article de recherche

Bounds for the blow-up time a class of integro-differential problem of parabolic type with variable reaction term
[Bornes sur le temps d’explosion pour une équation intégro-différentielle de type parabolique avec un terme réactif variable]

Rabil Ayazoglu ^1,² ; Ebubekir Akkoyunlu ¹

¹ Faculty of Education, Bayburt University, Bayburt, Turkey
² Institute of Mathematics and Mechanics of ANAS, Baku, Azerbaijan

Comptes Rendus. Mécanique, Volume 351 (2023), pp. 391-400.

Résumé
Abstract

Cet article traite du temps d’explosion des solutions d’un problème intégro-différentiel de type parabolique avec une croissance variable si l’explosion se produit. En utilisant la technique de l’inégalité différentielle, nous obtenons des bornes inférieures pour le temps d’explosion et des résultats d’existence globale sous certaines conditions sur l’exposant variable de réaction, le noyau de mémoire et la valeur initiale.

This paper is concerned with the blow-up time of the solutions to an integro-differential problem of parabolic type with variable growth if blow-up occurs. By using the differential inequality technique, we obtain lower bounds for the blow-up time and some global existence results under some conditions to variable exponent of reaction, memory kernel, and initial value.

Reçu le : 2023-04-18
Révisé le : 2023-10-02
Accepté le : 2023-10-17
Publié le : 2023-11-23

Zbl

DOI : 10.5802/crmeca.233

Keywords: Integro-differential problem, Parabolic, Variable reaction, Global existence, Blow-up, Lower bounds
Mot clés : Problème intégro-différentiel, Parabolique, Réaction variable, Existence globale, Explosion, Limites inférieures

Affiliations des auteurs :

Rabil Ayazoglu ^{1, 2} ; Ebubekir Akkoyunlu ¹

¹ Faculty of Education, Bayburt University, Bayburt, Turkey
² Institute of Mathematics and Mechanics of ANAS, Baku, Azerbaijan

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Rabil Ayazoglu and Ebubekir Akkoyunlu},
     title = {Bounds for the blow-up time a class of integro-differential problem of parabolic type with variable reaction term},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {391--400},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {351},
     year = {2023},
     doi = {10.5802/crmeca.233},
     zbl = {1498.35044},
     language = {en},
}

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Rabil Ayazoglu; Ebubekir Akkoyunlu. Bounds for the blow-up time a class of integro-differential problem of parabolic type with variable reaction term. Comptes Rendus. Mécanique, Volume 351 (2023), pp. 391-400. doi : 10.5802/crmeca.233. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.233/

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