Local manifolds for non-autonomous boundary Cauchy problems: existence and attractivity

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dc.citation.epage693
dc.citation.issue3
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage678
dc.contributor.affiliationУніверситет Мухаммеда І
dc.contributor.affiliationUniversity Mohammed I
dc.contributor.authorДжерруді, А.
dc.contributor.authorМуссі, М.
dc.contributor.authorJerroudi, A.
dc.contributor.authorMoussi, M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:33:00Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractУ цій роботі встановлено існування локальних стійких і локально нестійкихмноговидів для нелінійних крайових задач Коші. Крім того, отримані результати проілюстровано застосуванням до неавтономного рівняння Фішера–Колмогорова.
dc.description.abstractIn this work we establish the existence of local stable and local unstable manifolds for nonlinear boundary Cauchy problems. Moreover, we illustrate our results by an application to a non-autonomous Fisher–Kolmogorov equation.
dc.format.extent678-693
dc.format.pages16
dc.identifier.citationJerroudi A. Local manifolds for non-autonomous boundary Cauchy problems: existence and attractivity / A. Jerroudi, M. Moussi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 678–693.
dc.identifier.citationenJerroudi A. Local manifolds for non-autonomous boundary Cauchy problems: existence and attractivity / A. Jerroudi, M. Moussi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 678–693.
dc.identifier.doidoi.org/10.23939/mmc2022.03.678
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63465
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 3 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 3 (9), 2022
dc.relation.references[1] Boulite S., Maniar L., Moussi M. Wellposedness and asymptotic behaviour of nonautonomous boundary Cauchy problems. Forum Mathematicum. 18 (4), 611–638 (2006).
dc.relation.references[2] Doan T. S., Moussi M., Siegmund S. Integral Manifolds of Nonautonomous Boundary Cauchy Problems. Journal of Nonlinear Evolution Equations and Applications. 2012 (1), 1–15 (2012).
dc.relation.references[3] Jerroudi A., Moussi M. Invariant centre manifolds of non-autonomous boundary Cauchy problems (under review).
dc.relation.references[4] Moussi M. Pullback Attractors of Nonautonomous Boundary Cauchy Problems. Nonlinear Dynamics and Systems Theory. 14 (4), 383–394 (2014).
dc.relation.references[5] Kellermann H. Linear evolution equations with time dependent domain. Semesterbericht Funktionalanalysis T¨ubingen, Wintersemester. 16–44 (1986–1987).
dc.relation.references[6] Lan N. T. On non-autonomous functional differential equations. Journal of Mathematical Analysis and Applications. 239 (1), 158–174 (1999).
dc.relation.references[7] Jerroudi A., Moussi M. Stability and local attractivity for nonautonomous boundary Cauchy problems. Boletim da Sociedade Paranaense de Matem´atica (in press).
dc.relation.references[8] Minh N. V., R¨abiger F., Schnaubelt R. Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half line. Integral Equations and Operator Theory. 32 (3), 332–353 (1998).
dc.relation.references[9] Huy N. T. Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line. Journal of Functional Analysis. 235 (1), 330–354 (2006).
dc.relation.references[10] Schnaubelt R. Sufficient conditions for exponential stability and dichotomy of evolution equations. Forum Math. 11 (5), 543–566 (1999).
dc.relation.references[11] Schnaubelt R. Asymptotic behaviour of parabolic nonautonomous evolution equations. In: Functional Analytic Methods for Evolution Equations, 401–472. Springer Berlin Heidelberg, Berlin, Heidelberg (2004).
dc.relation.references[12] Greiner G. Perturbing the boundary conditions of a generator. Houston Journal of Mathematics. 13 (2), 213–229 (1987).
dc.relation.references[13] Moussi M. Well-posdness and asymptotic behavior of non-autonomous boundary Cauchy problems. Ph.D. thesis, Faculty of science, Oujda (2003).
dc.relation.references[14] Kato T. Linear evolution equations of “hyperbolic” type. J. Fac. Sci., Univ. Tokyo, Sect. I A. 17, 241–258 (1970).
dc.relation.references[15] Daleckii J. L., Krein M. G. Stability of solutions of differential equations in Banach space. Translations of Mathematical Monographs. Providence, Rhode Island (1994).
dc.relation.references[16] Brezis H. Analyse Fonctionnelle: Th´eorie et Applications. Masson (1987).
dc.relation.references[17] Engel K. J., Nagel R. One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics. 194, Springer-Verlag, New York (2000).
dc.relation.referencesen[1] Boulite S., Maniar L., Moussi M. Wellposedness and asymptotic behaviour of nonautonomous boundary Cauchy problems. Forum Mathematicum. 18 (4), 611–638 (2006).
dc.relation.referencesen[2] Doan T. S., Moussi M., Siegmund S. Integral Manifolds of Nonautonomous Boundary Cauchy Problems. Journal of Nonlinear Evolution Equations and Applications. 2012 (1), 1–15 (2012).
dc.relation.referencesen[3] Jerroudi A., Moussi M. Invariant centre manifolds of non-autonomous boundary Cauchy problems (under review).
dc.relation.referencesen[4] Moussi M. Pullback Attractors of Nonautonomous Boundary Cauchy Problems. Nonlinear Dynamics and Systems Theory. 14 (4), 383–394 (2014).
dc.relation.referencesen[5] Kellermann H. Linear evolution equations with time dependent domain. Semesterbericht Funktionalanalysis T¨ubingen, Wintersemester. 16–44 (1986–1987).
dc.relation.referencesen[6] Lan N. T. On non-autonomous functional differential equations. Journal of Mathematical Analysis and Applications. 239 (1), 158–174 (1999).
dc.relation.referencesen[7] Jerroudi A., Moussi M. Stability and local attractivity for nonautonomous boundary Cauchy problems. Boletim da Sociedade Paranaense de Matem´atica (in press).
dc.relation.referencesen[8] Minh N. V., R¨abiger F., Schnaubelt R. Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half line. Integral Equations and Operator Theory. 32 (3), 332–353 (1998).
dc.relation.referencesen[9] Huy N. T. Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line. Journal of Functional Analysis. 235 (1), 330–354 (2006).
dc.relation.referencesen[10] Schnaubelt R. Sufficient conditions for exponential stability and dichotomy of evolution equations. Forum Math. 11 (5), 543–566 (1999).
dc.relation.referencesen[11] Schnaubelt R. Asymptotic behaviour of parabolic nonautonomous evolution equations. In: Functional Analytic Methods for Evolution Equations, 401–472. Springer Berlin Heidelberg, Berlin, Heidelberg (2004).
dc.relation.referencesen[12] Greiner G. Perturbing the boundary conditions of a generator. Houston Journal of Mathematics. 13 (2), 213–229 (1987).
dc.relation.referencesen[13] Moussi M. Well-posdness and asymptotic behavior of non-autonomous boundary Cauchy problems. Ph.D. thesis, Faculty of science, Oujda (2003).
dc.relation.referencesen[14] Kato T. Linear evolution equations of "hyperbolic" type. J. Fac. Sci., Univ. Tokyo, Sect. I A. 17, 241–258 (1970).
dc.relation.referencesen[15] Daleckii J. L., Krein M. G. Stability of solutions of differential equations in Banach space. Translations of Mathematical Monographs. Providence, Rhode Island (1994).
dc.relation.referencesen[16] Brezis H. Analyse Fonctionnelle: Th´eorie et Applications. Masson (1987).
dc.relation.referencesen[17] Engel K. J., Nagel R. One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics. 194, Springer-Verlag, New York (2000).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectнеавтономна крайова задача Коші
dc.subjectлокальний многовид
dc.subjectнеавтономне рівняння Фішера–Колмогорова
dc.subjectnon-autonomous boundary Cauchy problem
dc.subjectlocal manifold
dc.subjectnon-autonomous Fisher–Kolmogorov equation
dc.titleLocal manifolds for non-autonomous boundary Cauchy problems: existence and attractivity
dc.title.alternativeЛокальні многовиди для неавтономних крайових задач Коші: існування та притягання
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 3