Semilinear periodic equation with arbitrary nonlinear growth and data measure: mathematical analysis and numerical simulation
| dc.citation.epage | 964 | |
| dc.citation.issue | 3 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 956 | |
| dc.contributor.affiliation | Університет Каді Айяд | |
| dc.contributor.affiliation | Cadi Ayyad University | |
| dc.contributor.author | Ель Габі, М. | |
| dc.contributor.author | Алаа, Х. | |
| dc.contributor.author | Алаа, Н. Е. | |
| dc.contributor.author | El Ghabi, M. | |
| dc.contributor.author | Alaa, H. | |
| dc.contributor.author | Alaa, N. E. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-04T12:17:33Z | |
| dc.date.created | 2023-02-28 | |
| dc.date.issued | 2023-02-28 | |
| dc.description.abstract | У цій роботі цікавимося існуванням, єдиністю та чисельним моделюванням слабких періодичних розв’язків для деяких напівлінійних еліптичних рівнянь із мірами даних та з довільними нелінійностями зростання. Оскільки дані не дуже регулярні, а зростання є довільним, необхідний новий підхід для аналізу цих типів рівнянь. Накінець, наведено відповідну чисельну схему дискретизації. Наведено декілька числових прикладів, які демонструють надійність запропонованого алгоритму. | |
| dc.description.abstract | In this work, we are interested in the existence, uniqueness, and numerical simulation of weak periodic solutions for some semilinear elliptic equations with data measures and with arbitrary growth of nonlinearities. Since the data are not very regular and the growths are arbitrary, a new approach is needed to analyze these types of equations. Finally, a suitable numerical discretization scheme is presented. Several numerical examples are given which show the robustness of our algorithm. | |
| dc.format.extent | 956-964 | |
| dc.format.pages | 9 | |
| dc.identifier.citation | El Ghabi M. Semilinear periodic equation with arbitrary nonlinear growth and data measure: mathematical analysis and numerical simulation / M. El Ghabi, H. Alaa, N. E. Alaa // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 3. — P. 956–964. | |
| dc.identifier.citationen | El Ghabi M. Semilinear periodic equation with arbitrary nonlinear growth and data measure: mathematical analysis and numerical simulation / M. El Ghabi, H. Alaa, N. E. Alaa // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 3. — P. 956–964. | |
| dc.identifier.doi | doi.org/10.23939/mmc2023.03.956 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/63532 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 3 (10), 2023 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 3 (10), 2023 | |
| dc.relation.references | [1] Alaa N. Quasilinear elliptic equations with arbitrary growth nonlinearity and data measures. Extracta Mathematicae. 11 (3), 405–411 (1996). | |
| dc.relation.references | [2] Alaa N., Iguernane M. Weak periodic solutions of some quasilinear parabolic equations with data measure. Journal of Inequalities in Pure and Applied Mathematics. 3 (3), 46 (2002). | |
| dc.relation.references | [3] Charkaoui A., Kouadri G., Selt O., Alaa N. Existence results of weak periodic solution for some quasilinear parabolic problem with L1 data. Annals of the University of Craiova, Mathematics and Computer Science Series. 46 (1), 66–77 (2019). | |
| dc.relation.references | [4] Charkaoui A., Kouadri G., Alaa N. Some Results on The Existence of Weak Periodic Solutions For Quasilinear Parabolic Systems With L1 Data. Boletim da Sociedade Paranaense de Matem´atica. 40, 1–15 (2022). | |
| dc.relation.references | [5] Elaassri A., Uahabi L. K., Charkaoui A., Alaa N. E., Mesbahi S. Existence of weak periodic solution for quasilinear parabolic problem with nonlinear boundary conditions. Annals of the University of Craiova, Mathematics and Computer Science Series. 46 (1), 1–13 (2019). | |
| dc.relation.references | [6] Alaa N. E., Charkaoui A., Elaassr A. Periodic parabolic problem with discontinuous coefficients. Mathematical Analysis and Numerical Simulation. 41 (6), 1251–1271 (2022). | |
| dc.relation.references | [7] Alaa H., El Ghabi M., Charkaoui A. Semilinear Periodic Parabolic Problem with Discontinuous Coefficients: Mathematical Anlysis and Numerical Simulation. Filomat. 37 (7), 2151–2164 (2023). | |
| dc.relation.references | [8] Canada A., Drabek P., Fonda A. Handbook of Differential Equations: Ordinary Differential Equations. North Holland (2008). | |
| dc.relation.references | [9] Farkas M. Periodic Motions. Springer, New York (1994). | |
| dc.relation.references | [10] De Coster C., Habets P. Chapter III – Relation with Degree Theory. Two-Point Boundary Value Problems: Lower and Upper Solutions. Mathematics in Science and Engineering. 205, 135–188 (2006). | |
| dc.relation.references | [11] Takemura K., Kametaka Y., Watanabe K., Nagai A., Yamagishi H. Sobolev type inequalities of timeperiodic boundary value problems for Heaviside and Thomson cables. Boundary Value Problems. 2012, 95 (2012). | |
| dc.relation.references | [12] Ciarlet P. G., Scitultz H., Vag R. S. Numerical Methods of High-Order Accuracy for Nonlinear Boundary Value Problems, IV. Periodic Boundary Conditions. Numerische Mathematik. 12, 266–279 (1968). | |
| dc.relation.references | [13] Aubin J.-P., Ekeland I. Applied Nonlinear Analysis. Wiley, Hoboken (1984). | |
| dc.relation.references | [14] Amjed D., Zaraiqati F., Al-Zoubhi H., Abu Hamma M. Numerical methods for finding periodic solutions of ordinary differential equations with strong nonlinearity. Journal of Mathematical and Computational Science. 11 (6), 6910–6922 (2021). | |
| dc.relation.references | [15] Samoilenko A. M. Certain questions of the theory of periodic and quasi-periodic systems. D.Sc. Dissertation, Kiev (1967). | |
| dc.relation.referencesen | [1] Alaa N. Quasilinear elliptic equations with arbitrary growth nonlinearity and data measures. Extracta Mathematicae. 11 (3), 405–411 (1996). | |
| dc.relation.referencesen | [2] Alaa N., Iguernane M. Weak periodic solutions of some quasilinear parabolic equations with data measure. Journal of Inequalities in Pure and Applied Mathematics. 3 (3), 46 (2002). | |
| dc.relation.referencesen | [3] Charkaoui A., Kouadri G., Selt O., Alaa N. Existence results of weak periodic solution for some quasilinear parabolic problem with L1 data. Annals of the University of Craiova, Mathematics and Computer Science Series. 46 (1), 66–77 (2019). | |
| dc.relation.referencesen | [4] Charkaoui A., Kouadri G., Alaa N. Some Results on The Existence of Weak Periodic Solutions For Quasilinear Parabolic Systems With L1 Data. Boletim da Sociedade Paranaense de Matem´atica. 40, 1–15 (2022). | |
| dc.relation.referencesen | [5] Elaassri A., Uahabi L. K., Charkaoui A., Alaa N. E., Mesbahi S. Existence of weak periodic solution for quasilinear parabolic problem with nonlinear boundary conditions. Annals of the University of Craiova, Mathematics and Computer Science Series. 46 (1), 1–13 (2019). | |
| dc.relation.referencesen | [6] Alaa N. E., Charkaoui A., Elaassr A. Periodic parabolic problem with discontinuous coefficients. Mathematical Analysis and Numerical Simulation. 41 (6), 1251–1271 (2022). | |
| dc.relation.referencesen | [7] Alaa H., El Ghabi M., Charkaoui A. Semilinear Periodic Parabolic Problem with Discontinuous Coefficients: Mathematical Anlysis and Numerical Simulation. Filomat. 37 (7), 2151–2164 (2023). | |
| dc.relation.referencesen | [8] Canada A., Drabek P., Fonda A. Handbook of Differential Equations: Ordinary Differential Equations. North Holland (2008). | |
| dc.relation.referencesen | [9] Farkas M. Periodic Motions. Springer, New York (1994). | |
| dc.relation.referencesen | [10] De Coster C., Habets P. Chapter III – Relation with Degree Theory. Two-Point Boundary Value Problems: Lower and Upper Solutions. Mathematics in Science and Engineering. 205, 135–188 (2006). | |
| dc.relation.referencesen | [11] Takemura K., Kametaka Y., Watanabe K., Nagai A., Yamagishi H. Sobolev type inequalities of timeperiodic boundary value problems for Heaviside and Thomson cables. Boundary Value Problems. 2012, 95 (2012). | |
| dc.relation.referencesen | [12] Ciarlet P. G., Scitultz H., Vag R. S. Numerical Methods of High-Order Accuracy for Nonlinear Boundary Value Problems, IV. Periodic Boundary Conditions. Numerische Mathematik. 12, 266–279 (1968). | |
| dc.relation.referencesen | [13] Aubin J.-P., Ekeland I. Applied Nonlinear Analysis. Wiley, Hoboken (1984). | |
| dc.relation.referencesen | [14] Amjed D., Zaraiqati F., Al-Zoubhi H., Abu Hamma M. Numerical methods for finding periodic solutions of ordinary differential equations with strong nonlinearity. Journal of Mathematical and Computational Science. 11 (6), 6910–6922 (2021). | |
| dc.relation.referencesen | [15] Samoilenko A. M. Certain questions of the theory of periodic and quasi-periodic systems. D.Sc. Dissertation, Kiev (1967). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2023 | |
| dc.subject | періодичний розв’язок | |
| dc.subject | напівлінійне рівняння | |
| dc.subject | метод оптимізації | |
| dc.subject | чисельне моделювання | |
| dc.subject | periodic solution | |
| dc.subject | semilinear equation | |
| dc.subject | optimisation method | |
| dc.subject | numerical simulation | |
| dc.title | Semilinear periodic equation with arbitrary nonlinear growth and data measure: mathematical analysis and numerical simulation | |
| dc.title.alternative | Напівлінійне періодичне рівняння з довільною нелінійністю зростання та мірою даних: математичний аналіз та чисельне моделювання | |
| dc.type | Article |
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