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
de Cássia D. S. Broche, Rita; Carvalho, Alexandre N.; Valero, José A non-autonomous scalar one-dimensional dissipative parabolic problem: the description of the dynamics. (English) Zbl 1425.35115 Nonlinearity 32, No. 12, 4912-4941 (2019). MSC: 35K91 35B32 35B41 37L30 PDFBibTeX XMLCite \textit{R. de Cássia D. S. Broche} et al., Nonlinearity 32, No. 12, 4912--4941 (2019; Zbl 1425.35115) Full Text: DOI arXiv
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
Caballero, Rubén; Carvalho, Alexandre N.; Marín-Rubio, Pedro; Valero, José Robustness of dynamically gradient multivalued dynamical systems. (English) Zbl 1408.37133 Discrete Contin. Dyn. Syst., Ser. B 24, No. 3, 1049-1077 (2019). MSC: 37L30 37L05 35B40 35B41 35K55 PDFBibTeX XMLCite \textit{R. Caballero} et al., Discrete Contin. Dyn. Syst., Ser. B 24, No. 3, 1049--1077 (2019; Zbl 1408.37133) Full Text: DOI
Cui, Hongyong; Langa, José A.; Li, Yangrong; Valero, José Attractors for multi-valued non-autonomous dynamical systems: relationship, characterization and robustness. (English) Zbl 1401.37085 Set-Valued Var. Anal. 26, No. 3, 493-530 (2018). MSC: 37L30 35B40 35B41 35K57 PDFBibTeX XMLCite \textit{H. Cui} et al., Set-Valued Var. Anal. 26, No. 3, 493--530 (2018; Zbl 1401.37085) Full Text: DOI
Valero, José On \(L^r\)-regularity of global attractors generated by strong solutions of reaction-diffusion equations. (English) Zbl 1379.37134 Appl. Math. Nonlinear Sci. 1, No. 2, 375-390 (2016). MSC: 37L30 35B40 35B41 35K55 35K57 37L05 PDFBibTeX XMLCite \textit{J. Valero}, Appl. Math. Nonlinear Sci. 1, No. 2, 375--390 (2016; Zbl 1379.37134) Full Text: DOI
da Costa, Henrique B.; Valero, José Morse decompositions and Lyapunov functions for dynamically gradient multivalued semiflows. (English) Zbl 1354.37075 Nonlinear Dyn. 84, No. 1, 19-34 (2016). MSC: 37L15 37L45 37L30 26E25 PDFBibTeX XMLCite \textit{H. B. da Costa} and \textit{J. Valero}, Nonlinear Dyn. 84, No. 1, 19--34 (2016; Zbl 1354.37075) Full Text: DOI
Caraballo, Tomás; Jara, Juan C.; Langa, José A.; Valero, José Morse decomposition of global attractors with infinite components. (English) Zbl 1366.37030 Discrete Contin. Dyn. Syst. 35, No. 7, 2845-2861 (2015). MSC: 37B25 35B40 35B41 37L30 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Discrete Contin. Dyn. Syst. 35, No. 7, 2845--2861 (2015; Zbl 1366.37030) Full Text: DOI
Anguiano, María; Caraballo, Tomás; Real, José; Valero, José Pullback attractors for nonautonomous dynamical systems. (English) Zbl 1332.37056 Pinelas, Sandra (ed.) et al., Differential and difference equations with applications. Contributions from the international conference on differential and difference equations and applications in honour of Ravi P. Agarwal, Ponta Delgada, Portugal, July 4–8, 2011. New York, NY: Springer (ISBN 978-1-4614-7332-9/hbk; 978-1-4614-7333-6/ebook). Springer Proceedings in Mathematics & Statistics 47, 217-225 (2013). MSC: 37L30 35K57 PDFBibTeX XMLCite \textit{M. Anguiano} et al., Springer Proc. Math. Stat. 47, 217--225 (2013; Zbl 1332.37056) Full Text: DOI
Caraballo, T.; Morillas, F.; Valero, J. Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity. (English) Zbl 1223.39010 J. Difference Equ. Appl. 17, No. 1-2, 161-184 (2011). Reviewer: Dora Selesi (Novi Sad) MSC: 39A50 39A30 37H10 37L30 37B25 37L55 60H10 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Difference Equ. Appl. 17, No. 1--2, 161--184 (2011; Zbl 1223.39010) Full Text: DOI Link
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
Anguiano, María; Caraballo, Tomás; Real, José; Valero, José Pullback attractors for reaction-diffusion equations in some unbounded domains with an \(H^{-1}\)-valued non-autonomous forcing term and without uniqueness of solutions. (English) Zbl 1197.35200 Discrete Contin. Dyn. Syst., Ser. B 14, No. 2, 307-326 (2010). MSC: 35Q35 35Q30 35K90 37L30 PDFBibTeX XMLCite \textit{M. Anguiano} et al., Discrete Contin. Dyn. Syst., Ser. B 14, No. 2, 307--326 (2010; Zbl 1197.35200) Full Text: DOI
Kloeden, P. E.; Valero, J. Attractors of set-valued partial differential equations under discretization. (English) Zbl 1177.65148 IMA J. Numer. Anal. 29, No. 3, 690-711 (2009). Reviewer: Dinh Nho Hao (Hanoi) MSC: 65M60 35K57 37L30 65M12 PDFBibTeX XMLCite \textit{P. E. Kloeden} and \textit{J. Valero}, IMA J. Numer. Anal. 29, No. 3, 690--711 (2009; Zbl 1177.65148) Full Text: DOI
Díaz, J. I.; Langa, J. A.; Valero, J. On the asymptotic behaviour of solutions of a stochastic energy balance climate model. (English) Zbl 1173.37051 Physica D 238, No. 9-10, 880-887 (2009). Reviewer: Henri Schurz (Carbondale) MSC: 37H10 37L30 37N99 60H15 60H30 PDFBibTeX XMLCite \textit{J. I. Díaz} et al., Physica D 238, No. 9--10, 880--887 (2009; Zbl 1173.37051) Full Text: DOI
Kapustyan, A. V.; Valero, J. Weak and strong attractors for the 3D Navier-Stokes system. (English) Zbl 1131.35056 J. Differ. Equations 240, No. 2, 249-278 (2007). Reviewer: Bruno Scarpellini (Basel) MSC: 35Q30 37L30 35B41 35K55 37B25 58C06 35B40 PDFBibTeX XMLCite \textit{A. V. Kapustyan} and \textit{J. Valero}, J. Differ. Equations 240, No. 2, 249--278 (2007; Zbl 1131.35056) 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
Arrieta, José M.; Rodríguez-Bernal, Aníbal; Valero, José Dynamics of a reaction-diffusion equation with a discontinuous nonlinearity. (English) Zbl 1185.37161 Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, No. 10, 2965-2984 (2006). MSC: 37L30 35K20 35K57 37L05 PDFBibTeX XMLCite \textit{J. M. Arrieta} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, No. 10, 2965--2984 (2006; Zbl 1185.37161) Full Text: DOI
Valero, José; Kapustyan, Alexey On the connectedness and asymptotic behaviour of solutions of reaction-diffusion systems. (English) Zbl 1169.35345 J. Math. Anal. Appl. 323, No. 1, 614-633 (2006). MSC: 35K57 35K55 35B41 35K20 37L30 PDFBibTeX XMLCite \textit{J. Valero} and \textit{A. Kapustyan}, J. Math. Anal. Appl. 323, No. 1, 614--633 (2006; Zbl 1169.35345) Full Text: DOI
Kapustyan, O. V.; Valero, J.; Pereguda, O. V. Random attractor for the reaction-diffusion equation perturbed by a stochastic càdlàg process. (Ukrainian, English) Zbl 1114.37028 Teor. Jmovirn. Mat. Stat. 73, 52-62 (2005); translation in Theory Probab. Math. Stat., Vol 73, 57-69 (2006). Reviewer: Mikhail P. Moklyachuk (Kyïv) MSC: 37H10 34F05 60H10 37L30 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Teor. Ĭmovirn. Mat. Stat. 73, 52--62 (2005; Zbl 1114.37028); translation in Theory Probab. Math. Stat., Vol 73, 57--69 (2006) Full Text: Link
Caraballo, T.; Langa, J. A.; Valero, J. Asymptotic behaviour of monotone multi-valued dynamical systems. (English) Zbl 1086.37042 Dyn. Syst. 20, No. 3, 301-321 (2005). MSC: 37L30 37C65 37C70 34K25 92C45 37N25 93C15 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Dyn. Syst. 20, No. 3, 301--321 (2005; Zbl 1086.37042) Full Text: DOI Link
Kapustyan, Alexei V.; Melnik, Valery S.; Valero, José Attractors of multivalued dynamical processes generated by phase-field equations. (English) Zbl 1063.37070 Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 7, 1969-1983 (2003). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37L30 37C70 35B41 35K55 35K85 35R70 PDFBibTeX XMLCite \textit{A. V. Kapustyan} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 7, 1969--1983 (2003; Zbl 1063.37070) Full Text: DOI
Caraballo, T.; Langa, J. A.; Valero, J. The dimension of attractors of nonautonomous partial differential equations. (English) Zbl 1047.35024 ANZIAM J. 45, No. 2, 207-222 (2003). Reviewer: Hans Crauel (Ilmenau) MSC: 35B41 35K60 37L30 PDFBibTeX XMLCite \textit{T. Caraballo} et al., ANZIAM J. 45, No. 2, 207--222 (2003; Zbl 1047.35024) Full Text: DOI
Valero, J.; Kapustyan, O. V.; Carballo, T.; Langa, J.; Mel’nyk, V. S. On global attractors from “\(-\infty\)” of multivalued dynamical processes in topological spaces. (Ukrainian. English summary) Zbl 1026.37063 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2003, No. 3, 7-10 (2003). Reviewer: I.O.Parasyuk (Kyïv) MSC: 37L30 47H20 54C60 54H20 PDFBibTeX XMLCite \textit{J. Valero} et al., Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2003, No. 3, 7--10 (2003; Zbl 1026.37063)
Valero, J.; Carballo, T.; Langa, J.; Mel’nyk, V. S. Attractors of nonautonomous and stochastic differential inclusions. (Ukrainian. English summary) Zbl 1026.37062 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2003, No. 2, 7-14 (2003). Reviewer: I.O.Parasyuk (Kyïv) MSC: 37L30 37H10 34G25 54C60 35R70 47H04 47H20 35R60 60H15 PDFBibTeX XMLCite \textit{J. Valero} et al., Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2003, No. 2, 7--14 (2003; Zbl 1026.37062)
Kapustyan, A. V.; Melnik, V. S.; Valero, J. Attractors of multivalued dynamical processes in topological space with inverse time. (English) Zbl 1048.37070 Nonlinear Bound. Value Probl. 12, 103-107 (2002). MSC: 37L30 35B41 PDFBibTeX XMLCite \textit{A. V. Kapustyan} et al., Nonlinear Bound. Value Probl. 12, 103--107 (2002; Zbl 1048.37070)
Caraballo, T.; Langa, J. A.; Valero, J. Approximation of attractors for multivalued random dynamical systems. (English) Zbl 1026.37046 Int. J. Math. Game Theory Algebra 11, No. 4, 67-92 (2001). MSC: 37H10 34G25 37L30 35R60 37L55 60H15 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Int. J. Math. Game Theory Algebra 11, No. 4, 67--92 (2001; Zbl 1026.37046)
Valero, J.; Mel’nik, V. S. Attractors of non-autonomous evolution inclusions in infinite-dimensional spaces. (Russian. English summary) Zbl 0983.35152 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2001, No. 10, 7-12 (2001). MSC: 35R70 37L30 47H04 PDFBibTeX XMLCite \textit{J. Valero} and \textit{V. S. Mel'nik}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2001, No. 10, 7--12 (2001; Zbl 0983.35152)
Caraballo, T.; Langa, J. A.; Valero, J. Global attractors for multivalued random dynamical systems generated by random differential inclusions with multiplicative noise. (English) Zbl 0987.60074 J. Math. Anal. Appl. 260, No. 2, 602-622 (2001). Reviewer: Hans Crauel (Ilmenau) MSC: 60H15 37H10 37L55 37L30 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Math. Anal. Appl. 260, No. 2, 602--622 (2001; Zbl 0987.60074) Full Text: DOI Link
Valero, J.; Mel’nik, V. S. On global attractors of nonautonomous evolution inclusions in Banach spaces. (English. Russian original) Zbl 1090.34579 Dokl. Math. 62, No. 3, 394-397 (2000); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 375, No. 6, 730-733 (2000). MSC: 34G25 34A60 37L30 PDFBibTeX XMLCite \textit{J. Valero} and \textit{V. S. Mel'nik}, Dokl. Math. 62, No. 3, 730--733 (2000; Zbl 1090.34579); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 375, No. 6, 730--733 (2000)
Valero, J. Finite and infinite-dimensional attractors of multivalued reaction-diffusion equations. (English) Zbl 0997.37058 Acta Math. Hung. 88, No. 3, 239-258 (2000). MSC: 37L30 35B41 35K57 PDFBibTeX XMLCite \textit{J. Valero}, Acta Math. Hung. 88, No. 3, 239--258 (2000; Zbl 0997.37058) Full Text: DOI
Valero, José Global attractors of reaction-diffusion equations without uniqueness. (English) Zbl 0966.37043 Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 1. Singapore: World Scientific. 653-655 (2000). MSC: 37L30 35B41 35K57 37N20 37N25 PDFBibTeX XMLCite \textit{J. Valero}, in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 1. Singapore: World Scientific. 653--655 (2000; Zbl 0966.37043)
Balibrea, Francisco; Valero, José On dimension of attractors of differential inclusions and reaction-diffusion equations. (English) Zbl 0963.37075 Discrete Contin. Dyn. Syst. 5, No. 3, 515-528 (1999). Reviewer: Messoud Efendiev (Berlin) MSC: 37L30 35B41 35K57 37L25 47H20 34G25 PDFBibTeX XMLCite \textit{F. Balibrea} and \textit{J. Valero}, Discrete Contin. Dyn. Syst. 5, No. 3, 515--528 (1999; Zbl 0963.37075) Full Text: DOI
Balibrea, Francisco; Valero, José On dimension of attractors of reaction-diffusion equations with periodic right-hand side. (English) Zbl 0951.37040 Ann. Math. Sil. 13, 61-71 (1999). Reviewer: Messoud Efendiev (Berlin) MSC: 37L30 37B55 35B40 35K57 PDFBibTeX XMLCite \textit{F. Balibrea} and \textit{J. Valero}, Ann. Math. Sil. 13, 61--71 (1999; Zbl 0951.37040)
Valero, José On locally compact attractors of dynamical systems. (English) Zbl 0935.37050 J. Math. Anal. Appl. 237, No. 1, 43-54 (1999). Reviewer: Messoud Efendiev (Berlin) MSC: 37L30 37N25 35B41 34A60 35K57 35Q58 PDFBibTeX XMLCite \textit{J. Valero}, J. Math. Anal. Appl. 237, No. 1, 43--54 (1999; Zbl 0935.37050) Full Text: DOI