Nonvariational double phase problems with variable exponents depending on the gradient of the solution with convection term

Ala Eddine Bahrouni; Anouar Bahrouni

doi:10.5802/crmath.788

Article de recherche - Équations aux dérivées partielles

Nonvariational double phase problems with variable exponents depending on the gradient of the solution with convection term
[Problèmes à double phase non variationnels avec exposants variables dépendant du gradient de la solution avec terme de convection]

Ala Eddine Bahrouni ¹ ; Anouar Bahrouni ¹

¹ Mathematics Department, Faculty of Sciences, University of Monastir, 5019 Monastir, Tunisia

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1277-1287

Abstract (VO)
Résumé

In this work, we study nonvariational double phase problems driven by a novel operator with variable exponents depending on the solutions and its gradient, along with a convection term. Using the Galerkin method, we prove the existence of solutions and apply a truncation technique to demonstrate multiplicity. Additionally, we address the uniqueness of solutions. The paper presents self-contained techniques to prove the multiplicity result, which may also be useful for addressing other problems with a convection term.

Dans ce travail, nous étudions des problèmes à double phase non variationnels gouvernés par un nouvel opérateur à exposants variables dépendant de la solution et de son gradient, auxquels s’ajoute un terme de convection. En utilisant la méthode de Galerkin, nous établissons l’existence de solutions et appliquons une technique de troncature pour démontrer la multiplicité. Nous abordons également la question de l’unicité des solutions. L’article présente des techniques autonomes permettant d’établir des résultats de multiplicité, lesquelles peuvent également être utiles pour traiter d’autres problèmes comportant un terme de convection.

Reçu le : 2024-12-09
Révisé le : 2025-07-16
Accepté le : 2025-08-18
Publié le : 2025-10-13

DOI : 10.5802/crmath.788

Classification : 35J20, 35J60, 35J70, 47J10, 46E35
Keywords: Double phase operators, multiplicity results, gradient term, variable exponents, nonvariational methods
Mots-clés : Opérateurs à double phase, résultats de multiplicité, terme en gradient, exposants variables, méthodes non variationnelles

Affiliations des auteurs :

Ala Eddine Bahrouni ¹ ; Anouar Bahrouni ¹

¹ Mathematics Department, Faculty of Sciences, University of Monastir, 5019 Monastir, Tunisia

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Ala Eddine Bahrouni and Anouar Bahrouni},
     title = {Nonvariational double phase problems with variable exponents depending on the gradient of the solution with convection term},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1277--1287},
     year = {2025},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     doi = {10.5802/crmath.788},
     language = {en},
}

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Ala Eddine Bahrouni; Anouar Bahrouni. Nonvariational double phase problems with variable exponents depending on the gradient of the solution with convection term. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1277-1287. doi: 10.5802/crmath.788

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