Existence and stability of solutions to nonlinear parabolic problems with perturbed gradient and measure data
| dc.citation.epage | 998 | |
| dc.citation.issue | 4 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 977 | |
| dc.contributor.affiliation | Університет Мохамеда Бен Абделлаха | |
| dc.contributor.affiliation | Університет Джозефа КІ-ЗЕРБО | |
| dc.contributor.affiliation | Mohamed Ben Abdellah University | |
| dc.contributor.affiliation | Universit´e Joseph KI-ZERBO | |
| dc.contributor.author | Бенбубкер, М. Б. | |
| dc.contributor.author | Траоре, У. | |
| dc.contributor.author | Benboubker, M. B. | |
| dc.contributor.author | Traore, U. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-24T09:14:09Z | |
| dc.date.created | 2022-02-28 | |
| dc.date.issued | 2022-02-28 | |
| dc.description.abstract | У цій статті доводиться існування ентропійного розв’язку нелінійних параболічних рівнянь з дифузними даними радонівської міри, який не навантажує множини нульової p(·)-ємності та неоднорідної крайової умови Неймана. За допомогою методики часової дискретизації аналізуються питання існування, єдиності та стійкості. Функціональна постановка включає простори Лебега та Соболєва зі змінними показниками. | |
| dc.description.abstract | In this paper we prove the existence of an entropy solution to nonlinear parabolic equations with diffuse Radon measure data which does not charge the sets of zero p(⋅)-capacity and nonhomogeneous Neumann boundary condition. By a time discretization technique we analyze existence, the uniqueness and the stability questions. The functional setting involves Lebesgue and Sobolev spaces with variable exponents. | |
| dc.format.extent | 977-998 | |
| dc.format.pages | 22 | |
| dc.identifier.citation | Benboubker M. B. Existence and stability of solutions to nonlinear parabolic problems with perturbed gradient and measure data / M. B. Benboubker, U. Traore // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 4. — P. 977–998. | |
| dc.identifier.citationen | Benboubker M. B. Existence and stability of solutions to nonlinear parabolic problems with perturbed gradient and measure data / M. B. Benboubker, U. Traore // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 4. — P. 977–998. | |
| dc.identifier.doi | doi.org/10.23939/mmc2022.04.977 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/64235 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 4 (9), 2022 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 4 (9), 2022 | |
| dc.relation.references | [1] Benboubker M. B., Ouaro S., Traor´e U. Entropy solutions for nonlinear nonhomogeneous Neumann problems involving the generalized p(x)-Laplace operator and measure data. J. Nonlinear Evol. Eqns. Appl. 5, 53–76 (2015). | |
| dc.relation.references | [2] El Hachimi A., Igbida J., Jamea A. Existence result for nonlinear parabolic problems with L1-data. Applicationes Mathematicae. 37, 483–508 (2010). | |
| dc.relation.references | [3] Benzekri F., El Hachimi A. Doubly nonlinear parabolic equations related to the p-Laplacian operator: Semi-discretization. Electronic Journal of Differential Equations. 2003 (113), 1–14 (2003). | |
| dc.relation.references | [4] Eden E., Michaux B., Rakotoson J. M. Semi-discretized nonlinear evolution equations as dynamical systems and error analysis. Indiana University Mathematics Journal. 39 (3), 737–783 (1990). | |
| dc.relation.references | [5] R˚aˇziˇcka M. Electrorheological fluids: modeling and mathematical theory. Lecture Notes in Mathematics. Vol. 1748. Springer–Verlag, Berlin, Heidelberg (2000). | |
| dc.relation.references | [6] Antontsev S. N., Shmarev S. I. A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions. Nonlinear Analysis: Theory, Methods & Applications. 60 (3), 515–545 (2005). | |
| dc.relation.references | [7] Boccardo L., Gallou¨et T., Orsina L. Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data. Annales de l’Institut Henri Poincar´e C. 13 (5), 539–551 (1996). | |
| dc.relation.references | [8] Abdellaoui M., Azroul E., Ouaro S., Traor´e U. Nonlinear parabolic capacity and renormalized solutions for PDEs with diffuse measure data and variable exponent. Annals of the University of Craiova, Mathematics and Computer Science Series. 46 (2), 269–297 (2010). | |
| dc.relation.references | [9] Azroul E., Benboubker M. B., Redwane H. Yazough C. Renormalized solutions for a class of nonlinear parabolic equations without sign condition involving nonstandard growth. Annals of the University of Craiova, Mathematics and Computer Science Series. 41 (1), 69–87 (2014). | |
| dc.relation.references | [10] Benboubker M. B., Nassouri E., Ouaro S., Traor´e U. Renormalized solutions for a p(·)-Laplacian equation with Neumann nonhomogeneous boundary condition involving diffuse measure data and variable exponent. Moroccan Journal of Pure and Applied Analysis. 8 (1), 163–178 (2022). | |
| dc.relation.references | [11] Ouaro S., Traor´e U. Nonlinear parabolic problem with variable exponent and measure data. Journal of Nonlinear Evolution Equations and Applications. 2020 (5), 65–93 (2020). | |
| dc.relation.references | [12] Redwane H. Nonlinear parabolic equation with variable exponents and diffuse measure data. Journal of Nonlinear Evolution Equations and Applications. 2019 (6), 95–114 (2019). | |
| dc.relation.references | [13] Droniou J., Porretta A., Prignet A. Parabolic capacity and soft measures for nonlinear equations. Potential Analysis. 19 (2), 99–161 (2003). | |
| dc.relation.references | [14] Azroul E., Benboubker M. B., Rhoudaf M. Entropy solution for some p(x)-Quasilinear problems with righthand side measure. African Diaspora Journal of Mathematics. New Series. 13 (2), 23–44 (2012). | |
| dc.relation.references | [15] Igbida N., Ouaro S., Soma S. Elliptic problem involving diffuse measure data. Journal of Differential Equations. 253 (12), 3159–3183 (2012). | |
| dc.relation.references | [16] Nyanquini I., Ouaro S., Soma S. Entropy solution to nonlinear multivalued elliptic problem with variable exponents and measure data. Annals of the University of Craiova, Mathematics and Computer Science Series. 40 (2), 174–198 (2013). | |
| dc.relation.references | [17] Ouaro S., Ouedraogo A., Soma S. Multivalued homogeneous Neumann problem involving diffuse measure data and variable exponent. Nonlinear Dynamics and Systems Theory. 16 (1), 102–114 (2016). | |
| dc.relation.references | [18] Br´ezis H. Analyse Fonctionnelle: Th´eorie et Applications. Paris Masson (1983). | |
| dc.relation.references | [19] Diening L., Harjulehto P., H¨ast¨o P., Ruˇziˇcka M. Lebesgue and Sobolev spaces with variable exponents. Lecture Notes in Mathematics. Vol. 2017, Springer–Verlag, Heidelberg (2011). | |
| dc.relation.references | [20] Fan X. L., Zhao D. On the generalized Orlicz–Sobolev space Wk,p(x) (Ω). J. Gansu Educ. Coll. 12 (1), 1–6 (1998). | |
| dc.relation.references | [21] Zhao D., Qiang W. J., Fan X. L. On generalized Orlicz spaces Lp(x) (Ω). J. Gansu Sci. 9 (2), 1–7 (1997). | |
| dc.relation.references | [22] Wang L.-L., Fan Y.-H., Ge W.-G. Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator. Nonlinear Analysis: Theory, Methods & Applications. 71 (9), 4259–4270 (2009). | |
| dc.relation.references | [23] Yao J. Solutions for Neumann boundary value problems involving p(x)-Laplace operator. Nonlinear Analysis: Theory, Methods & Applications. 68 (5), 1271–1283 (2008). | |
| dc.relation.references | [24] Azroul E., Benboubker M. B., Ouaro S. Entropy solutions for nonlinear nonhomogeneous Neumann problems involving the generalized p(x)-Laplace operator. Journal of Applied Analysis & Computation. 3 (2), 105–121 (2013). | |
| dc.relation.references | [25] Halmos P. R. Measure Theory. Springer, New York (1950). | |
| dc.relation.references | [26] Gagneux G., Madaune-Tort M. Analyse math´ematique de mod`eles non lin´eaires de l’ing´enierie p´etroli`ere. Math´ematiques et Applications. 22 (1996). | |
| dc.relation.references | [27] B´enilan P., Boccardo L., Gallou¨et T., Gariepy R., Pierre M., Vazquez J. L. An L1 theory of existence and uniqueness of nonlinear elliptic equations. Annali Della Scuola Normale Superiore Di Pisa Classe di Scienze. 22 (2), 241–273 (1995). | |
| dc.relation.references | [28] Andreu F., Maz´on J. M., Segura de Le´on S., Toledo J. Existence and uniqueness for a degenerate parabolic equation with L1-data. Transactions of the American Mathematical Society. 351 (1), 285–306 (1999). | |
| dc.relation.references | [29] Andreu F., Igbida N., Maz´on J. M., Toledo J. L1 existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions. Annales de l’Institut Henri Poincar´e C. 24 (1), 61–89 (2007). | |
| dc.relation.references | [30] Ouaro S., Soma S. Weak and entropy solutions to nonlinear Neumann boundary-problems with variable exponent. Complex Variables and Elliptic Equations. 56 (7–9), 829–851 (2011). | |
| dc.relation.references | [31] Jamea A., El Hachimi A. Uniqueness result of entropy solution to nonlinear Neumann problems with variable exponent and L1 data. Journal of Nonlinear Evolution Equations and Applications. 2017 (2), 13–25 (2017). | |
| dc.relation.references | [32] Abassi A., El Hachimi A., Jamea A. Entropy solutions to nonlinear Neumann problems with L1-data. International Journal of Mathematics and Statistics. 2 (S08), 4–17 (2008). | |
| dc.relation.referencesen | [1] Benboubker M. B., Ouaro S., Traor´e U. Entropy solutions for nonlinear nonhomogeneous Neumann problems involving the generalized p(x)-Laplace operator and measure data. J. Nonlinear Evol. Eqns. Appl. 5, 53–76 (2015). | |
| dc.relation.referencesen | [2] El Hachimi A., Igbida J., Jamea A. Existence result for nonlinear parabolic problems with L1-data. Applicationes Mathematicae. 37, 483–508 (2010). | |
| dc.relation.referencesen | [3] Benzekri F., El Hachimi A. Doubly nonlinear parabolic equations related to the p-Laplacian operator: Semi-discretization. Electronic Journal of Differential Equations. 2003 (113), 1–14 (2003). | |
| dc.relation.referencesen | [4] Eden E., Michaux B., Rakotoson J. M. Semi-discretized nonlinear evolution equations as dynamical systems and error analysis. Indiana University Mathematics Journal. 39 (3), 737–783 (1990). | |
| dc.relation.referencesen | [5] R˚aˇziˇcka M. Electrorheological fluids: modeling and mathematical theory. Lecture Notes in Mathematics. Vol. 1748. Springer–Verlag, Berlin, Heidelberg (2000). | |
| dc.relation.referencesen | [6] Antontsev S. N., Shmarev S. I. A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions. Nonlinear Analysis: Theory, Methods & Applications. 60 (3), 515–545 (2005). | |
| dc.relation.referencesen | [7] Boccardo L., Gallou¨et T., Orsina L. Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data. Annales de l’Institut Henri Poincar´e P. 13 (5), 539–551 (1996). | |
| dc.relation.referencesen | [8] Abdellaoui M., Azroul E., Ouaro S., Traor´e U. Nonlinear parabolic capacity and renormalized solutions for PDEs with diffuse measure data and variable exponent. Annals of the University of Craiova, Mathematics and Computer Science Series. 46 (2), 269–297 (2010). | |
| dc.relation.referencesen | [9] Azroul E., Benboubker M. B., Redwane H. Yazough C. Renormalized solutions for a class of nonlinear parabolic equations without sign condition involving nonstandard growth. Annals of the University of Craiova, Mathematics and Computer Science Series. 41 (1), 69–87 (2014). | |
| dc.relation.referencesen | [10] Benboubker M. B., Nassouri E., Ouaro S., Traor´e U. Renormalized solutions for a p(·)-Laplacian equation with Neumann nonhomogeneous boundary condition involving diffuse measure data and variable exponent. Moroccan Journal of Pure and Applied Analysis. 8 (1), 163–178 (2022). | |
| dc.relation.referencesen | [11] Ouaro S., Traor´e U. Nonlinear parabolic problem with variable exponent and measure data. Journal of Nonlinear Evolution Equations and Applications. 2020 (5), 65–93 (2020). | |
| dc.relation.referencesen | [12] Redwane H. Nonlinear parabolic equation with variable exponents and diffuse measure data. Journal of Nonlinear Evolution Equations and Applications. 2019 (6), 95–114 (2019). | |
| dc.relation.referencesen | [13] Droniou J., Porretta A., Prignet A. Parabolic capacity and soft measures for nonlinear equations. Potential Analysis. 19 (2), 99–161 (2003). | |
| dc.relation.referencesen | [14] Azroul E., Benboubker M. B., Rhoudaf M. Entropy solution for some p(x)-Quasilinear problems with righthand side measure. African Diaspora Journal of Mathematics. New Series. 13 (2), 23–44 (2012). | |
| dc.relation.referencesen | [15] Igbida N., Ouaro S., Soma S. Elliptic problem involving diffuse measure data. Journal of Differential Equations. 253 (12), 3159–3183 (2012). | |
| dc.relation.referencesen | [16] Nyanquini I., Ouaro S., Soma S. Entropy solution to nonlinear multivalued elliptic problem with variable exponents and measure data. Annals of the University of Craiova, Mathematics and Computer Science Series. 40 (2), 174–198 (2013). | |
| dc.relation.referencesen | [17] Ouaro S., Ouedraogo A., Soma S. Multivalued homogeneous Neumann problem involving diffuse measure data and variable exponent. Nonlinear Dynamics and Systems Theory. 16 (1), 102–114 (2016). | |
| dc.relation.referencesen | [18] Br´ezis H. Analyse Fonctionnelle: Th´eorie et Applications. Paris Masson (1983). | |
| dc.relation.referencesen | [19] Diening L., Harjulehto P., H¨ast¨o P., Ruˇziˇcka M. Lebesgue and Sobolev spaces with variable exponents. Lecture Notes in Mathematics. Vol. 2017, Springer–Verlag, Heidelberg (2011). | |
| dc.relation.referencesen | [20] Fan X. L., Zhao D. On the generalized Orlicz–Sobolev space Wk,p(x) (Ω). J. Gansu Educ. Coll. 12 (1), 1–6 (1998). | |
| dc.relation.referencesen | [21] Zhao D., Qiang W. J., Fan X. L. On generalized Orlicz spaces Lp(x) (Ω). J. Gansu Sci. 9 (2), 1–7 (1997). | |
| dc.relation.referencesen | [22] Wang L.-L., Fan Y.-H., Ge W.-G. Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator. Nonlinear Analysis: Theory, Methods & Applications. 71 (9), 4259–4270 (2009). | |
| dc.relation.referencesen | [23] Yao J. Solutions for Neumann boundary value problems involving p(x)-Laplace operator. Nonlinear Analysis: Theory, Methods & Applications. 68 (5), 1271–1283 (2008). | |
| dc.relation.referencesen | [24] Azroul E., Benboubker M. B., Ouaro S. Entropy solutions for nonlinear nonhomogeneous Neumann problems involving the generalized p(x)-Laplace operator. Journal of Applied Analysis & Computation. 3 (2), 105–121 (2013). | |
| dc.relation.referencesen | [25] Halmos P. R. Measure Theory. Springer, New York (1950). | |
| dc.relation.referencesen | [26] Gagneux G., Madaune-Tort M. Analyse math´ematique de mod`eles non lin´eaires de l’ing´enierie p´etroli`ere. Math´ematiques et Applications. 22 (1996). | |
| dc.relation.referencesen | [27] B´enilan P., Boccardo L., Gallou¨et T., Gariepy R., Pierre M., Vazquez J. L. An L1 theory of existence and uniqueness of nonlinear elliptic equations. Annali Della Scuola Normale Superiore Di Pisa Classe di Scienze. 22 (2), 241–273 (1995). | |
| dc.relation.referencesen | [28] Andreu F., Maz´on J. M., Segura de Le´on S., Toledo J. Existence and uniqueness for a degenerate parabolic equation with L1-data. Transactions of the American Mathematical Society. 351 (1), 285–306 (1999). | |
| dc.relation.referencesen | [29] Andreu F., Igbida N., Maz´on J. M., Toledo J. L1 existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions. Annales de l’Institut Henri Poincar´e P. 24 (1), 61–89 (2007). | |
| dc.relation.referencesen | [30] Ouaro S., Soma S. Weak and entropy solutions to nonlinear Neumann boundary-problems with variable exponent. Complex Variables and Elliptic Equations. 56 (7–9), 829–851 (2011). | |
| dc.relation.referencesen | [31] Jamea A., El Hachimi A. Uniqueness result of entropy solution to nonlinear Neumann problems with variable exponent and L1 data. Journal of Nonlinear Evolution Equations and Applications. 2017 (2), 13–25 (2017). | |
| dc.relation.referencesen | [32] Abassi A., El Hachimi A., Jamea A. Entropy solutions to nonlinear Neumann problems with L1-data. International Journal of Mathematics and Statistics. 2 (S08), 4–17 (2008). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2022 | |
| dc.subject | нелінійна параболічна задача | |
| dc.subject | змінні показники | |
| dc.subject | ентропійний розв’язок | |
| dc.subject | крайові умови типу Неймана | |
| dc.subject | напівдискретизація | |
| dc.subject | міра Радона | |
| dc.subject | nonlinear parabolic problem | |
| dc.subject | variable exponents | |
| dc.subject | entropy solution | |
| dc.subject | Neumann–type boundary conditions | |
| dc.subject | semi-discretization | |
| dc.subject | Radon measure | |
| dc.title | Existence and stability of solutions to nonlinear parabolic problems with perturbed gradient and measure data | |
| dc.title.alternative | Існування та стійкість розв’язків нелінійних параболічних задач зі збуреним градієнтом та вимірювальними даними | |
| dc.type | Article |
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