Xu, Jiaohui; Caraballo, Tomás; Valero, José Asymptotic behavior of nonlocal partial differential equations with long time memory. (English) Zbl 1498.35088 Discrete Contin. Dyn. Syst., Ser. S 15, No. 10, 3059-3078 (2022). MSC: 35B40 35K20 35R09 37L30 45K05 PDFBibTeX XMLCite \textit{J. Xu} et al., Discrete Contin. Dyn. Syst., Ser. S 15, No. 10, 3059--3078 (2022; Zbl 1498.35088) Full Text: DOI
Xu, Jiaohui; Caraballo, Tomás; Valero, José Asymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusion. (English) Zbl 1489.35018 J. Differ. Equations 327, 418-447 (2022). MSC: 35B40 35B41 35K20 35K58 35R10 37L30 45K05 PDFBibTeX XMLCite \textit{J. Xu} et al., J. Differ. Equations 327, 418--447 (2022; Zbl 1489.35018) Full Text: DOI
Garrido-Atienza, María J.; Schmalfuß, Björn; Valero, José Attractors for a random evolution equation with infinite memory: an application. (English) Zbl 1474.37099 Sadovnichiy, Victor A. (ed.) et al., Modern mathematics and mechanics. Fundamentals, problems and challenges. Cham: Springer. Underst. Complex Syst., 215-236 (2019). MSC: 37L55 37L30 60H15 35K57 45R05 PDFBibTeX XMLCite \textit{M. J. Garrido-Atienza} et al., in: Modern mathematics and mechanics. Fundamentals, problems and challenges. Cham: Springer. 215--236 (2019; Zbl 1474.37099) Full Text: DOI
Kapustyan, Olexiy V.; Kasyanov, Pavlo O.; Valero, José; Zgurovsky, Mikhail Z. Attractors of multivalued semi-flows generated by solutions of optimal control problems. (English) Zbl 1473.35060 Discrete Contin. Dyn. Syst., Ser. B 24, No. 3, 1229-1242 (2019). Reviewer: Bixiang Wang (Socorro) MSC: 35B41 35B40 35K55 35Q30 35Q35 37B25 58C06 35Q93 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Discrete Contin. Dyn. Syst., Ser. B 24, No. 3, 1229--1242 (2019; Zbl 1473.35060) Full Text: DOI
Valero, José; Schmalfuß, Björn; Garrido-Atienza, María J.; Caraballo, Tomás Attractors for a random evolution equation with infinite memory: theoretical results. (English) Zbl 1359.60080 Discrete Contin. Dyn. Syst., Ser. B 22, No. 5, 1779-1800 (2017). MSC: 60H15 60H25 35K40 35K41 35K55 PDFBibTeX XMLCite \textit{J. Valero} et al., Discrete Contin. Dyn. Syst., Ser. B 22, No. 5, 1779--1800 (2017; Zbl 1359.60080) Full Text: DOI
Simsen, Jacson; Valero, José Characterization of pullback attractors for multivalued nonautonomous dynamical systems. (English) Zbl 1362.37037 Sadovnichiy, Victor A. (ed.) et al., Advances in dynamical systems and control. Cham: Springer (ISBN 978-3-319-40672-5/hbk; 978-3-319-40673-2/ebook). Studies in Systems, Decision and Control 69, 179-195 (2016). MSC: 37B25 37B55 35K57 PDFBibTeX XMLCite \textit{J. Simsen} and \textit{J. Valero}, Stud. Syst. Decis. Control 69, 179--195 (2016; Zbl 1362.37037) Full Text: DOI
Caraballo, Tomás; Morillas, Francisco; Valero, José Attractors for non-autonomous retarded lattice dynamical systems. (English) Zbl 1329.34119 Nonauton. Dyn. Syst. 2, 31-51 (2015). MSC: 34K31 34K05 37C60 34K09 34K25 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Nonauton. Dyn. Syst. 2, 31--51 (2015; Zbl 1329.34119) Full Text: DOI
Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Valero, José; Zgurovsky, Mikhail Z. Structure of uniform global attractor for general non-autonomous reaction-diffusion system. (English) Zbl 1323.35084 Zgurovsky, Mikhail Z. (ed.) et al., Continuous and distributed systems. Theory and applications. Cham: Springer (ISBN 978-3-319-03145-3/hbk; 978-3-319-03146-0/ebook). Solid Mechanics and Its Applications 211, 163-180 (2014). MSC: 35K57 35B41 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Solid Mech. Appl. 211, 163--180 (2014; Zbl 1323.35084) Full Text: DOI
Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Valero, José Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term. (English) Zbl 1304.35118 Discrete Contin. Dyn. Syst. 34, No. 10, 4155-4182 (2014). MSC: 35B41 35B40 35K55 37L25 58C06 35K57 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Discrete Contin. Dyn. Syst. 34, No. 10, 4155--4182 (2014; Zbl 1304.35118) Full Text: DOI arXiv
Kloeden, P. E.; Marín-Rubio, P.; Valero, J. The envelope attractor of non-strict multivalued dynamical systems with application to the 3D Navier-Stokes and reaction-diffusion equations. (English) Zbl 1277.35066 Set-Valued Var. Anal. 21, No. 3, 517-540 (2013). Reviewer: Cheng He (Beijing) MSC: 35B41 35B40 35K55 35K57 35Q30 37B25 58C06 PDFBibTeX XMLCite \textit{P. E. Kloeden} et al., Set-Valued Var. Anal. 21, No. 3, 517--540 (2013; Zbl 1277.35066) Full Text: DOI
Anguiano, María; Caraballo, Tomás; Real, José; Valero, José Pullback attractors for a nonautonomous integro-differential equation with memory in some unbounded domains. (English) Zbl 1270.34178 Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 3, Article ID 1350042, 24 p. (2013). MSC: 34K30 35R10 34K25 35B41 PDFBibTeX XMLCite \textit{M. Anguiano} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 3, Article ID 1350042, 24 p. (2013; Zbl 1270.34178) Full Text: DOI
Kapustyan, O. V.; Pan’kov, A. V.; Valero, J. On the existence and connectedness of a global attractor for solutions of the three-dimensional Bénard system that satisfy a system of energy inequalities. (English. Russian original) Zbl 1291.35222 J. Math. Sci., New York 191, No. 3, 388-402 (2013); translation from Neliniĭni Kolyvannya 15, No. 3, 354-366 (2012). MSC: 35Q35 35B41 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., J. Math. Sci., New York 191, No. 3, 388--402 (2013; Zbl 1291.35222); translation from Neliniĭni Kolyvannya 15, No. 3, 354--366 (2012) Full Text: DOI
Caraballo, Tomás; Morillas, F.; Valero, J. Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities. (English) Zbl 1248.37045 J. Differ. Equations 253, No. 2, 667-693 (2012). Reviewer: Vladimir Răsvan (Craiova) MSC: 37H10 60H10 35B41 37L55 37B25 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Differ. Equations 253, No. 2, 667--693 (2012; Zbl 1248.37045) Full Text: DOI
Anguiano, M.; Morillas, F.; Valero, J. On the Kneser property for reaction-diffusion equations in some unbounded domains with an \(H^{ - 1}\)-valued non-autonomous forcing term. (English) Zbl 1237.35016 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2623-2636 (2012). MSC: 35B40 35B41 35K57 35K55 37B25 58C06 PDFBibTeX XMLCite \textit{M. Anguiano} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2623--2636 (2012; Zbl 1237.35016) Full Text: DOI
Marín-Rubio, Pedro; Real, José; Valero, José Pullback attractors for a two-dimensional Navier-Stokes model in an infinite delay case. (English) Zbl 1218.35045 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 5, 2012-2030 (2011). Reviewer: Oleg Dementiev (Chelyabinsk) MSC: 35B41 35K55 35Q30 34D45 PDFBibTeX XMLCite \textit{P. Marín-Rubio} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 5, 2012--2030 (2011; Zbl 1218.35045) Full Text: DOI
Kapustyan, O. V.; Kasyanov, P. O.; Valero, J. Pullback attractors for a class of extremal solutions of the 3D Navier-Stokes system. (English) Zbl 1206.35048 J. Math. Anal. Appl. 373, No. 2, 535-547 (2011). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35B41 35Q35 49J20 35Q93 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., J. Math. Anal. Appl. 373, No. 2, 535--547 (2011; Zbl 1206.35048) Full Text: DOI
Balibrea, F.; Caraballo, T.; Kloeden, P. E.; Valero, J. Recent developments in dynamical systems: three perspectives. (English) Zbl 1202.37003 Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 9, 2591-2636 (2010). MSC: 37-02 37A35 37C05 37C60 37C70 37H15 37N10 PDFBibTeX XMLCite \textit{F. Balibrea} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 9, 2591--2636 (2010; Zbl 1202.37003) Full Text: DOI
Caraballo, T.; Garrido-Atienza, M. J.; Schmalfuß, B.; Valero, J. Global attractor for a non-autonomous integro-differential equation in materials with memory. (English) Zbl 1194.35071 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 1, 183-201 (2010). MSC: 35B41 35K58 35K57 35R10 35R09 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 1, 183--201 (2010; Zbl 1194.35071) Full Text: DOI Link
Kloeden, P. E.; Valero, J. The weak connectedness of the attainability set of weak solutions of the three-dimensional Navier-Stokes equations. (English) Zbl 1143.35082 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 463, No. 2082, 1491-1508 (2007). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35Q30 37C30 37N10 76D05 76D03 PDFBibTeX XMLCite \textit{P. E. Kloeden} and \textit{J. Valero}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 463, No. 2082, 1491--1508 (2007; Zbl 1143.35082) Full Text: DOI
Caraballo, T.; Marín-Rubio, P.; Valero, J. Attractors for differential equations with unbounded delays. (English) Zbl 1135.34040 J. Differ. Equations 239, No. 2, 311-342 (2007). Reviewer: Bernhard Lani-Wayda (Giessen) MSC: 34K25 37L30 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Differ. Equations 239, No. 2, 311--342 (2007; Zbl 1135.34040) Full Text: DOI Link