Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak–spaces
| dc.citation.epage | 600 | |
| dc.citation.issue | 4 | |
| dc.citation.spage | 584 | |
| dc.contributor.affiliation | Університет Сіді Мохаммеда Бен Абделли | |
| dc.contributor.affiliation | Sidi Mohammed Ben Abdellah University | |
| dc.contributor.author | Аберкі, А. | |
| dc.contributor.author | Ельмасуді, М. | |
| dc.contributor.author | Хаммумі, М. | |
| dc.contributor.author | Aberqi, A. | |
| dc.contributor.author | Elmassoudi, M. | |
| dc.contributor.author | Hammoumi, M. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2023-11-01T07:49:35Z | |
| dc.date.available | 2023-11-01T07:49:35Z | |
| dc.date.created | 2021-03-01 | |
| dc.date.issued | 2021-03-01 | |
| dc.description.abstract | У цій статті досліджується клас нелінійних еволюційних рівнянь зі загасанням, що виникають у гідродинаміці та реології. Нелінійний член монотонний і має опуклий потенціал, але нестандартно зростає. Відповідним функціональним каркасом для таких рівнянь є модульні простори Музейлака. Доведено існування та єдиність слабкого розв’язку, використовуючи наближений підхід та комбінуючи внутрішнє наближення зі зворотною схемою Ейлера, а також дано апріорну оцінку похибки часової напівдискретизації. | |
| dc.description.abstract | In this paper, a class of nonlinear evolution equations with damping arising in fluid dynamics and rheology is studied. The nonlinear term is monotone and possesses a convex potential but exhibits non-standard growth. The appropriate functional framework for such equations is the modularly Museilak-spaces. The existence and uniqueness of a weak solution are proved using an approximation approach by combining an internal approximation with the backward Euler scheme, also a priori error estimate for the temporal semi-discretization is given. | |
| dc.format.extent | 584-600 | |
| dc.format.pages | 17 | |
| dc.identifier.citation | Aberqi A. Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak–spaces / A. Aberqi, M. Elmassoudi, M. Hammoumi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 4. — P. 584–600. | |
| dc.identifier.citationen | Aberqi A. Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak–spaces / A. Aberqi, M. Elmassoudi, M. Hammoumi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 4. — P. 584–600. | |
| dc.identifier.doi | 10.23939/mmc2021.04.584 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/60443 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 4 (8), 2021 | |
| dc.relation.references | [1] Gwiazda P., Swierczewska-Gwiazda A., Wr´oblewska A. Monotonicity methods in generalized Orlicz spaces ˙ for a class of non-Newtonian fluids. Math. Methods Appl. Sci. 33 (2), 125–137 (2010). | |
| dc.relation.references | [2] Musielak J. Modular spaces and Orlicz spaces. Lecture Notes in Math. (1983). | |
| dc.relation.references | [3] Del Vecchio T., Posteraro M. R. Existence and regularity results for nonlinear elliptic equations with measure data. Adv. Differential Equations. 1 (5), 899–917 (1996). | |
| dc.relation.references | [4] Di Nardo R., Feo F., Guib´e O. Existence result for nonlinear parabolic equations with lower order terms. Analysis and Applications. 9 (2), 161–186 (2011). | |
| dc.relation.references | [5] Blanchard D., Murat F., Redwane H. Existence and uniqueness of a renormalized solution for fairly general class of non linear parabolic problems. Journal of Differential Equations. 177 (2), 331–374 (2001). | |
| dc.relation.references | [6] Aberqi A., Bennouna J., Mekkour M., Redwane H. Renormalized solution for a nonlinear parabolic equation with lower order terms. The Australian Journal of Mathematical Analysis and Applications. 10 (1), 1–15 (2013). | |
| dc.relation.references | [7] Aberqi A., Bennouna J., Mekkour M., Redwane H. Nonlinear parabolic inequality with lower order terms. Applicable Analysis. 96 (12), 2102–2117 (2017). | |
| dc.relation.references | [8] Aharouch L., Bennouna J. Existence and uniqueness of solutions of unilateral problems in Orlicz spaces. Nonlinear Analysis: Theory, Methods & Applications. 72 (9–10), 3553–3565 (2010). | |
| dc.relation.references | [9] Aberqi A., Bennouna J., Elmassoudi M., Hammoumi M. Existence and uniqueness of a renormalized solution of parabolic problems in Orlicz spaces. Monatshefte f¨ur Mathematik. 189, 195–219 (2019). | |
| dc.relation.references | [10] Mukminov F. Kh. Uniqueness of the renormalized solutions to the cauchy problem for an anistropic parabolic equation. Ufa Mathematical Journal. 8 (2), 44–57 (2016). | |
| dc.relation.references | [11] Mukminov F. Kh. Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev–Orlicz spaces. Sbornik: Mathematics. 208 (8), 1187–1206 (2017). | |
| dc.relation.references | [12] Emmrich E., Wroblewska-Kaminska A. Convergence of a full discretization of quasi-linear parabolic equations in isotropic and anisotropic Orlicz spaces. SIAM Journal on Numerical Analysis. 51 (2), 1163–1184 (2013). | |
| dc.relation.references | [13] Ruf A. M. Convergence of a full discretization for a second-order nonlinear elastodynamic equation in isotropic and anisotropic Orlicz spaces. Zeitschrift f¨ur angewandte Mathematik und Physik. 68, 118 (2017). | |
| dc.relation.references | [14] Elmassoudi M., Aberqi A., Bennouna J. Existence of Entropy Solutions in Musielak–Orlicz Spaces Via a Sequence of Penalized Equations. Boletim da Sociedade Paranaense de Matem´atica. 38 (6), 203–238 (2020). | |
| dc.relation.references | [15] Ait Khellou M., Benkirane A., Douiri S. M. Some properties of Musielak spaces with only the log-H¨older continuity condition and application. Annals of Functional Analysis. 11, 1062–1080 (2020). | |
| dc.relation.references | [16] Benkirane A., Sidi El Vally M. Some approximation properties in Musielak–Orlicz–Sobolev spaces. Thai journal of mathematics. 10 (2), 371–381 (2012). | |
| dc.relation.references | [17] Elemine Vall M. S. B., Ahmed A., Touzani A., Benkirane A. Existence of entropy solutions for nonlinear elliptic equations in Musielak framework with L 1 data. Boletim da Sociedade Paranaense de Matem´atica. 36 (1), 125–150 (2018). | |
| dc.relation.references | [18] Gossez J. P. Some approximation properties in Orlicz–Sobolev spaces. Studia Mathematica. 74 (1), 17–24 (1982). | |
| dc.relation.references | [19] Ciarlet P. G. Finite element methods (Part 1). Handbook of Numerical Analysis. Vol. 2. North-Holland, Amsterdam (1991). | |
| dc.relation.references | [20] Diening L., R ˙uˇziˇcka M. Interpolation operators in Orlicz–Sobolev spaces. Numerische Mathematik. 107, 107–129 (2007). | |
| dc.relation.references | [21] Aberqi A., Bennouna J., Elmassoudi M. Nonlinear elliptic equations with some measure data in Musielak–Orlicz space. Nonlinear Dynamics and Systems Theory. 19 (2), 227–242 (2019). | |
| dc.relation.references | [22] Gossez J.-P. Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients. Trans. Amer. Math. Soc. 190, 163–205 (1974). | |
| dc.relation.referencesen | [1] Gwiazda P., Swierczewska-Gwiazda A., Wr´oblewska A. Monotonicity methods in generalized Orlicz spaces ˙ for a class of non-Newtonian fluids. Math. Methods Appl. Sci. 33 (2), 125–137 (2010). | |
| dc.relation.referencesen | [2] Musielak J. Modular spaces and Orlicz spaces. Lecture Notes in Math. (1983). | |
| dc.relation.referencesen | [3] Del Vecchio T., Posteraro M. R. Existence and regularity results for nonlinear elliptic equations with measure data. Adv. Differential Equations. 1 (5), 899–917 (1996). | |
| dc.relation.referencesen | [4] Di Nardo R., Feo F., Guib´e O. Existence result for nonlinear parabolic equations with lower order terms. Analysis and Applications. 9 (2), 161–186 (2011). | |
| dc.relation.referencesen | [5] Blanchard D., Murat F., Redwane H. Existence and uniqueness of a renormalized solution for fairly general class of non linear parabolic problems. Journal of Differential Equations. 177 (2), 331–374 (2001). | |
| dc.relation.referencesen | [6] Aberqi A., Bennouna J., Mekkour M., Redwane H. Renormalized solution for a nonlinear parabolic equation with lower order terms. The Australian Journal of Mathematical Analysis and Applications. 10 (1), 1–15 (2013). | |
| dc.relation.referencesen | [7] Aberqi A., Bennouna J., Mekkour M., Redwane H. Nonlinear parabolic inequality with lower order terms. Applicable Analysis. 96 (12), 2102–2117 (2017). | |
| dc.relation.referencesen | [8] Aharouch L., Bennouna J. Existence and uniqueness of solutions of unilateral problems in Orlicz spaces. Nonlinear Analysis: Theory, Methods & Applications. 72 (9–10), 3553–3565 (2010). | |
| dc.relation.referencesen | [9] Aberqi A., Bennouna J., Elmassoudi M., Hammoumi M. Existence and uniqueness of a renormalized solution of parabolic problems in Orlicz spaces. Monatshefte f¨ur Mathematik. 189, 195–219 (2019). | |
| dc.relation.referencesen | [10] Mukminov F. Kh. Uniqueness of the renormalized solutions to the cauchy problem for an anistropic parabolic equation. Ufa Mathematical Journal. 8 (2), 44–57 (2016). | |
| dc.relation.referencesen | [11] Mukminov F. Kh. Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev–Orlicz spaces. Sbornik: Mathematics. 208 (8), 1187–1206 (2017). | |
| dc.relation.referencesen | [12] Emmrich E., Wroblewska-Kaminska A. Convergence of a full discretization of quasi-linear parabolic equations in isotropic and anisotropic Orlicz spaces. SIAM Journal on Numerical Analysis. 51 (2), 1163–1184 (2013). | |
| dc.relation.referencesen | [13] Ruf A. M. Convergence of a full discretization for a second-order nonlinear elastodynamic equation in isotropic and anisotropic Orlicz spaces. Zeitschrift f¨ur angewandte Mathematik und Physik. 68, 118 (2017). | |
| dc.relation.referencesen | [14] Elmassoudi M., Aberqi A., Bennouna J. Existence of Entropy Solutions in Musielak–Orlicz Spaces Via a Sequence of Penalized Equations. Boletim da Sociedade Paranaense de Matem´atica. 38 (6), 203–238 (2020). | |
| dc.relation.referencesen | [15] Ait Khellou M., Benkirane A., Douiri S. M. Some properties of Musielak spaces with only the log-H¨older continuity condition and application. Annals of Functional Analysis. 11, 1062–1080 (2020). | |
| dc.relation.referencesen | [16] Benkirane A., Sidi El Vally M. Some approximation properties in Musielak–Orlicz–Sobolev spaces. Thai journal of mathematics. 10 (2), 371–381 (2012). | |
| dc.relation.referencesen | [17] Elemine Vall M. S. B., Ahmed A., Touzani A., Benkirane A. Existence of entropy solutions for nonlinear elliptic equations in Musielak framework with L 1 data. Boletim da Sociedade Paranaense de Matem´atica. 36 (1), 125–150 (2018). | |
| dc.relation.referencesen | [18] Gossez J. P. Some approximation properties in Orlicz–Sobolev spaces. Studia Mathematica. 74 (1), 17–24 (1982). | |
| dc.relation.referencesen | [19] Ciarlet P. G. Finite element methods (Part 1). Handbook of Numerical Analysis. Vol. 2. North-Holland, Amsterdam (1991). | |
| dc.relation.referencesen | [20] Diening L., R ˙uˇziˇcka M. Interpolation operators in Orlicz–Sobolev spaces. Numerische Mathematik. 107, 107–129 (2007). | |
| dc.relation.referencesen | [21] Aberqi A., Bennouna J., Elmassoudi M. Nonlinear elliptic equations with some measure data in Musielak–Orlicz space. Nonlinear Dynamics and Systems Theory. 19 (2), 227–242 (2019). | |
| dc.relation.referencesen | [22] Gossez J.-P. Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients. Trans. Amer. Math. Soc. 190, 163–205 (1974). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2021 | |
| dc.subject | дискретний розв’язок | |
| dc.subject | параболічне рівняння | |
| dc.subject | слабкий розв’язок | |
| dc.subject | простори Мусейлака | |
| dc.subject | нестандартне зростання | |
| dc.subject | зворотня схема Ейлера | |
| dc.subject | внутрішнє наближення | |
| dc.subject | discrete solution | |
| dc.subject | parabolic equation | |
| dc.subject | weak solution | |
| dc.subject | Museilak-spaces | |
| dc.subject | nonstandard growth | |
| dc.subject | backward Euler scheme | |
| dc.subject | intern approximations | |
| dc.title | Discrete solution for the nonlinear parabolic equations with diffusion terms in Museilak–spaces | |
| dc.title.alternative | Дискретний розв’язок нелінійних параболічних рівнянь із дифузійними членами в просторах Мусейлака | |
| dc.type | Article |
Files
License bundle
1 - 1 of 1