Anisotropic parabolic problem with variable exponent and regular data
| dc.citation.epage | 535 | |
| dc.citation.issue | 3 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 519 | |
| dc.contributor.affiliation | Університет Мсіла | |
| dc.contributor.affiliation | University of M’sila | |
| dc.contributor.author | Мечетер, Р. | |
| dc.contributor.author | Rabah, Mecheter | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-04T11:33:05Z | |
| dc.date.created | 2022-02-28 | |
| dc.date.issued | 2022-02-28 | |
| dc.description.abstract | У цій роботі досліджується існування слабких розв’язків для класу нелінійних параболічних рівнянь із регулярними даними у просторах Соболєва зі змінною експонентою. Доводиться “версія” слабкої оцінки простору Лебега, яка сходить до “Lions J. L. Quelques m´ethodes de r´esolution des probl`emes aux limites. Dunod, Paris (1969)”, для параболічних рівнянь з анізотропними постійними показниками (pi(·) = pi). | |
| dc.description.abstract | In this paper, we study the existence of weak solutions for a class of nonlinear parabolic equations with regular data in the setting of variable exponent Sobolev spaces. We prove a "version" of a weak Lebesgue space estimate that goes back to "Lions J. L. Quelques méthodes de résolution des problèmes aux limites. Dunod, Paris (1969)" for parabolic equations with anisotropic constant exponents (pi(⋅)=pi). | |
| dc.format.extent | 519-535 | |
| dc.format.pages | 17 | |
| dc.identifier.citation | Rabah M. Anisotropic parabolic problem with variable exponent and regular data / Rabah Mecheter // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 519–535. | |
| dc.identifier.citationen | Rabah M. Anisotropic parabolic problem with variable exponent and regular data / Rabah Mecheter // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 519–535. | |
| dc.identifier.doi | doi.org/10.23939/mmc2022.03.519 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/63477 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 3 (9), 2022 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 3 (9), 2022 | |
| dc.relation.references | [1] Almeida A., Harjulehto P., H¨ast¨o P., Lukkari T. Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces. Annali di Matematica Pura ed Applicata. 194 (4), 405–424 (2015). | |
| dc.relation.references | [2] Antontsev S., Shmarev S. Anisotropic Parabolic Equations with variable non linearity. Publicacions Matem`atiques. 53 (2), 355–399 (2009). | |
| dc.relation.references | [3] Atik Y. Introduction aux probl`emes elliptiques quasi-lin´eaires а donn´ee mesure. Cours sp´eciaux de l’ENSKouba, Alger (1998). | |
| dc.relation.references | [4] Bendahmane M., Wittbold P. Renormalized solutions for nonlinear elliptic equations with variable exponents and L1-data. Nonlinear Analysis: Theory, Methods & Applications. 70 (2), 567–583 (2009). | |
| dc.relation.references | [5] Boureanu M.-M., V´elez-Santiago A. Fine regularity for elliptic and parabolic anisotropic Robin problems with variable exponents. Journal of Differential Equations. 266 (12), 8164–8232 (2019). | |
| dc.relation.references | [6] Brezis H. Analyse fonctionnelle: Th´eorie et applications. Masson, Paris (1983). | |
| dc.relation.references | [7] Brezis H. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, New York (2011). | |
| dc.relation.references | [8] Fan X. Anisotropic variable exponent Sobolev spaces and p(x) → Laplacian equations. Complex Variables and Elliptic Equations. 56 (7–9), 623–642 (2011). | |
| dc.relation.references | [9] Fan X. Local boundedness of quasi-minimizers of integral functionals with variable exponent anisotropic growth and applications. Nonlinear Differential Equations and Applications. 17 (5), 619–637 (2010). | |
| dc.relation.references | [10] Lions J. L. Quelques m´ethodes de r´esolution des probl`emes aux limites. Dunod, Paris (1969). | |
| dc.relation.references | [11] Mokhtari F. Regularity of the Solution to Nonlinear Anisotropic Elliptic Equations with Variable Exponents and Irregular Data. Mediterranean Journal of Mathematics. 14, 141 (2017). | |
| dc.relation.references | [12] Mokhtari F. Anisotropic parabolic problems with measur data. Differential Equations and Applications. 2, 123–150 (2010). | |
| dc.relation.references | [13] Mokhtari F. Probl`emes paraboliques anisotropes а donn´ees dans un espace d’Orlicz ou mesures. Th`ese de doctorat. (2011). | |
| dc.relation.references | [14] Prignet A. Probl`emes elliptiques et paraboliques dans un cadre non variationnel. UMPA-ENS Lyon France (1997). | |
| dc.relation.references | [15] Rakotoson J. M. A compactness lemma for quasilinear problems: application to parabolic equations. Journal of Functional Analysis. 106 (2), 358–374 (1992). | |
| dc.relation.references | [16] Simon J. Compact sets in the space Lp (0, T ; B). Annali di Matematica Pura ed Applicata. 146, 65–96 (1987). | |
| dc.relation.references | [17] Stampacchia G. Le probl`eme de Dirichlet pour les `equations elliptiques du seconde ordre `а coefficientes discontinus. Annales de l’Institut Fourier. 15 (1), 189–258 (1965). | |
| dc.relation.references | [18] Troisi M. Theoremi di inclusione per Spazi di Sobolev non isotropi. Ricerche di Matematica. 18, 3–24 (1969). | |
| dc.relation.referencesen | [1] Almeida A., Harjulehto P., H¨ast¨o P., Lukkari T. Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces. Annali di Matematica Pura ed Applicata. 194 (4), 405–424 (2015). | |
| dc.relation.referencesen | [2] Antontsev S., Shmarev S. Anisotropic Parabolic Equations with variable non linearity. Publicacions Matem`atiques. 53 (2), 355–399 (2009). | |
| dc.relation.referencesen | [3] Atik Y. Introduction aux probl`emes elliptiques quasi-lin´eaires a donn´ee mesure. Cours sp´eciaux de l’ENSKouba, Alger (1998). | |
| dc.relation.referencesen | [4] Bendahmane M., Wittbold P. Renormalized solutions for nonlinear elliptic equations with variable exponents and L1-data. Nonlinear Analysis: Theory, Methods & Applications. 70 (2), 567–583 (2009). | |
| dc.relation.referencesen | [5] Boureanu M.-M., V´elez-Santiago A. Fine regularity for elliptic and parabolic anisotropic Robin problems with variable exponents. Journal of Differential Equations. 266 (12), 8164–8232 (2019). | |
| dc.relation.referencesen | [6] Brezis H. Analyse fonctionnelle: Th´eorie et applications. Masson, Paris (1983). | |
| dc.relation.referencesen | [7] Brezis H. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, New York (2011). | |
| dc.relation.referencesen | [8] Fan X. Anisotropic variable exponent Sobolev spaces and p(x) → Laplacian equations. Complex Variables and Elliptic Equations. 56 (7–9), 623–642 (2011). | |
| dc.relation.referencesen | [9] Fan X. Local boundedness of quasi-minimizers of integral functionals with variable exponent anisotropic growth and applications. Nonlinear Differential Equations and Applications. 17 (5), 619–637 (2010). | |
| dc.relation.referencesen | [10] Lions J. L. Quelques m´ethodes de r´esolution des probl`emes aux limites. Dunod, Paris (1969). | |
| dc.relation.referencesen | [11] Mokhtari F. Regularity of the Solution to Nonlinear Anisotropic Elliptic Equations with Variable Exponents and Irregular Data. Mediterranean Journal of Mathematics. 14, 141 (2017). | |
| dc.relation.referencesen | [12] Mokhtari F. Anisotropic parabolic problems with measur data. Differential Equations and Applications. 2, 123–150 (2010). | |
| dc.relation.referencesen | [13] Mokhtari F. Probl`emes paraboliques anisotropes a donn´ees dans un espace d’Orlicz ou mesures. Th`ese de doctorat. (2011). | |
| dc.relation.referencesen | [14] Prignet A. Probl`emes elliptiques et paraboliques dans un cadre non variationnel. UMPA-ENS Lyon France (1997). | |
| dc.relation.referencesen | [15] Rakotoson J. M. A compactness lemma for quasilinear problems: application to parabolic equations. Journal of Functional Analysis. 106 (2), 358–374 (1992). | |
| dc.relation.referencesen | [16] Simon J. Compact sets in the space Lp (0, T ; B). Annali di Matematica Pura ed Applicata. 146, 65–96 (1987). | |
| dc.relation.referencesen | [17] Stampacchia G. Le probl`eme de Dirichlet pour les `equations elliptiques du seconde ordre `a coefficientes discontinus. Annales de l’Institut Fourier. 15 (1), 189–258 (1965). | |
| dc.relation.referencesen | [18] Troisi M. Theoremi di inclusione per Spazi di Sobolev non isotropi. Ricerche di Matematica. 18, 3–24 (1969). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2022 | |
| dc.subject | анізотропні параболічні | |
| dc.subject | нелінійні параболічні рівняння | |
| dc.subject | регулярні дані | |
| dc.subject | anisotropic parabolic | |
| dc.subject | nonlinear parabolic equations | |
| dc.subject | regular data | |
| dc.title | Anisotropic parabolic problem with variable exponent and regular data | |
| dc.title.alternative | Анізотропна параболічна задача зі змінним показником регулярними даними | |
| dc.type | Article |
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