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
Brzeźniak, Z.; Caraballo, T.; Langa, J. A.; Li, Y.; Łukaszewicz, G.; Real, J. Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains. (English) Zbl 1283.35075 J. Differ. Equations 255, No. 11, 3897-3919 (2013). MSC: 35Q35 35B41 35R60 37C70 PDFBibTeX XMLCite \textit{Z. Brzeźniak} et al., J. Differ. Equations 255, No. 11, 3897--3919 (2013; Zbl 1283.35075) Full Text: DOI arXiv
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
Caraballo, Tomás; Real, José; Márquez, Antonio M. Three-dimensional system of globally modified Navie-Stokes equations with delay. (English) Zbl 1202.35153 Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 9, 2869-2883 (2010). MSC: 35Q30 35B41 35R10 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 9, 2869--2883 (2010; Zbl 1202.35153) Full Text: DOI
Anguiano, María; Caraballo, Tomás; Real, José Existence of pullback attractor for a reaction – diffusion equation in some unbounded domains with non-autonomous forcing term in \(H^{-1}\). (English) Zbl 1202.35034 Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 9, 2645-2656 (2010). MSC: 35B41 35K57 PDFBibTeX XMLCite \textit{M. Anguiano} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 9, 2645--2656 (2010; Zbl 1202.35034) 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
Caraballo, Tomás; Real, José; Kloeden, Peter E. Addendum to the paper “Unique strong solutions and \(V\)-attractors of a three dimensional system of globally modified Navier-Stokes equations”. (English) Zbl 1221.35273 Adv. Nonlinear Stud. 10, No. 1, 245-247 (2010). MSC: 35Q30 35K90 37L30 76M10 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Adv. Nonlinear Stud. 10, No. 1, 245--247 (2010; Zbl 1221.35273)
Anguiano, M.; Caraballo, T.; Real, J. An exponential growth condition in \(H^{2}\) for the pullback attractor of a non-autonomous reaction-diffusion equation. (English) Zbl 1187.35017 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 11, 4071-4075 (2010). MSC: 35B41 35K57 35K20 35K58 PDFBibTeX XMLCite \textit{M. Anguiano} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 11, 4071--4075 (2010; Zbl 1187.35017) Full Text: DOI
Anguiano, M.; Caraballo, T.; Real, J. \(H^{2}\)-boundedness of the pullback attractor for a non-autonomous reaction-diffusion equation. (English) Zbl 1180.35117 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 2, 876-880 (2010). MSC: 35B41 35Q35 35K57 35K58 35K20 PDFBibTeX XMLCite \textit{M. Anguiano} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 2, 876--880 (2010; Zbl 1180.35117) Full Text: DOI
Caraballo, T.; Márquez-Durán, A. M.; Real, J. Asymptotic behaviour of the three-dimensional \(\alpha\)-Navier-Stokes model with locally Lipschitz delay forcing terms. (English) Zbl 1238.35084 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e-Suppl., e271-e282 (2009). MSC: 35Q30 76D03 35B40 35R10 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e271--e282 (2009; Zbl 1238.35084) Full Text: DOI
Caraballo, Tomás; Kloeden, Peter E.; Real, José Invariant measures and statistical solutions of the globally modified Navier-Stokes equations. (English) Zbl 1187.35152 Discrete Contin. Dyn. Syst., Ser. B 10, No. 4, 761-781 (2008). MSC: 35Q30 35K90 37L30 35B65 35B41 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Discrete Contin. Dyn. Syst., Ser. B 10, No. 4, 761--781 (2008; Zbl 1187.35152) Full Text: DOI
Caraballo, T.; Real, J.; Chueshov, I. D. Pullback attractors for stochastic heat equations in materials with memory. (English) Zbl 1152.60044 Discrete Contin. Dyn. Syst., Ser. B 9, No. 3-4, 525-539 (2008). Reviewer: Carles Rovira (Barcelona) MSC: 60H15 35B25 35B40 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Discrete Contin. Dyn. Syst., Ser. B 9, No. 3--4, 525--539 (2008; Zbl 1152.60044) Full Text: DOI
Caraballo, T.; Márquez-Durán, A. M.; Real, J. Asymptotic behaviour of the three-dimensional \(\alpha \)-Navier-Stokes model with delays. (English) Zbl 1187.35151 J. Math. Anal. Appl. 340, No. 1, 410-423 (2008). Reviewer: Pavel Burda (Praha) MSC: 35Q30 35B40 35B35 76D05 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Math. Anal. Appl. 340, No. 1, 410--423 (2008; Zbl 1187.35151) Full Text: DOI
Caraballo, T.; Chueshov, I. D.; Marín-Rubio, P.; Real, J. Existence and asymptotic behaviour for stochastic heat equations with multiplicative noise in materials with memory. (English) Zbl 1125.60057 Discrete Contin. Dyn. Syst. 18, No. 2-3, 253-270 (2007). MSC: 60H15 35K40 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Discrete Contin. Dyn. Syst. 18, No. 2--3, 253--270 (2007; Zbl 1125.60057) Full Text: DOI
Caraballo, T.; Real, J.; Shaikhet, L. Method of Lyapunov functionals construction in stability of delay evolution equations. (English) Zbl 1178.34087 J. Math. Anal. Appl. 334, No. 2, 1130-1145 (2007). MSC: 34K20 34K30 35R10 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Math. Anal. Appl. 334, No. 2, 1130--1145 (2007; Zbl 1178.34087) Full Text: DOI Link
Caraballo, Tomás; Real, José; Taniguchi, Takeshi On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier-Stokes equations. (English) Zbl 1149.35397 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 462, No. 2066, 459-479 (2006). MSC: 35Q30 35R60 60H15 76D05 76D06 76M35 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 462, No. 2066, 459--479 (2006; Zbl 1149.35397) Full Text: DOI
Caraballo, Tomás; Real, José; Kloeden, Peter E. Unique strong solutions and \(V\)-attractors of a three dimensional system of globally modified Navier-Stokes equations. (English) Zbl 1220.35115 Adv. Nonlinear Stud. 6, No. 3, 411-436 (2006); addendum ibid. 10, No. 1, 245-247 (2010). Reviewer: Bruno Scarpellini (Basel) MSC: 35Q30 35K90 37L30 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Adv. Nonlinear Stud. 6, No. 3, 411--436 (2006; Zbl 1220.35115) Full Text: DOI
Caraballo, T.; Garrido-Atienza, M. J.; Real, J. Stability of nonlinear functional stochastic evolution equations of second order in time. (English) Zbl 1127.60060 J. Math. Sci., New York 138, No. 1, 5377-5389 (2006). Reviewer: Maria Stolarczyk (Katowice) MSC: 60H20 34K50 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Math. Sci., New York 138, No. 1, 5377--5389 (2006; Zbl 1127.60060) Full Text: DOI Link
Caraballo, T.; Márquez-Durán, A. M.; Real, José Pullback and forward attractors for a 3D LANS-\(\alpha\) model with delay. (English) Zbl 1119.35104 Discrete Contin. Dyn. Syst. 15, No. 2, 559-578 (2006). Reviewer: Bruno Scarpellini (Basel) MSC: 35R10 35Q35 37L30 35B41 76D05 37N10 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Discrete Contin. Dyn. Syst. 15, No. 2, 559--578 (2006; Zbl 1119.35104) Full Text: DOI
Caraballo, Tomás; Kloeden, Peter E.; Real, José Discretization of asymptotically stable stationary solutions of delay differential equations with a random stationary delay. (English) Zbl 1125.34064 J. Dyn. Differ. Equations 18, No. 4, 863-880 (2006). Reviewer: Vigirdas Mackevičius (Vilnius) MSC: 34K50 34K28 34K25 60G10 65C20 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Dyn. Differ. Equations 18, No. 4, 863--880 (2006; Zbl 1125.34064) Full Text: DOI Link
Caraballo, Tomas; Marquez-Duran, Antonio M.; Real, Jose The asymptotic behaviour of a stochastic 3D LANS-\(\alpha\) model. (English) Zbl 1097.60053 Appl. Math. Optimization 53, No. 2, 141-161 (2006). MSC: 60H15 35Q35 60H30 35R15 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Appl. Math. Optim. 53, No. 2, 141--161 (2006; Zbl 1097.60053) Full Text: DOI
Caraballo, T.; Łukaszewicz, G.; Real, J. Pullback attractors for asymptotically compact non-autonomous dynamical systems. (English) Zbl 1128.37019 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 64, No. 3, 484-498 (2006). Reviewer: Messoud A. Efendiev (Berlin) MSC: 37C70 37C60 35Q35 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 64, No. 3, 484--498 (2006; Zbl 1128.37019) Full Text: DOI Link
Caraballo, Tomás; Łukaszewicz, Grzegorz; Real, José Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains. (English) Zbl 1085.37054 C. R., Math., Acad. Sci. Paris 342, No. 4, 263-268 (2006). MSC: 37L30 35Q30 35B41 37N10 37B55 74D05 PDFBibTeX XMLCite \textit{T. Caraballo} et al., C. R., Math., Acad. Sci. Paris 342, No. 4, 263--268 (2006; Zbl 1085.37054) Full Text: DOI
Caraballo, T.; Real, J. Asymptotic behaviour and attractors of 2D-Navier-Stokes models with delays. (English) Zbl 1105.34332 Dumortier, Freddy (ed.) et al., EQUADIFF 2003. Proceedings of the international conference on differential equations, Hasselt, Belgium, July 22–26, 2003. Hackensack, NJ: World Scientific (ISBN 981-256-169-2/hbk). 827-832 (2005). MSC: 34K30 35B41 76D05 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{J. Real}, in: EQUADIFF 2003. Proceedings of the international conference on differential equations, Hasselt, Belgium, July 22--26, 2003. Hackensack, NJ: World Scientific. 827--832 (2005; Zbl 1105.34332)
Caraballo, T.; Márquez-Durán, A. M.; Real, J. On the stochastic 3D-Lagrangian averaged Navier-Stokes \(\alpha\)-model with finite delay. (English) Zbl 1083.35142 Stoch. Dyn. 5, No. 2, 189-200 (2005). Reviewer: Stanisław Wedrychowicz (Rzeszów) MSC: 35R60 60H15 35Q30 76D05 76M35 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stoch. Dyn. 5, No. 2, 189--200 (2005; Zbl 1083.35142) Full Text: DOI
Caraballo, T.; Real, J. Attractors for 2D-Navier-Stokes models with delays. (English) Zbl 1068.35088 J. Differ. Equations 205, No. 2, 271-297 (2004). Reviewer: Bruno Scarpellini (Basel) MSC: 35Q30 35R10 47H20 37L30 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{J. Real}, J. Differ. Equations 205, No. 2, 271--297 (2004; Zbl 1068.35088) Full Text: DOI
Caraballo, T.; Kloeden, P. E.; Real, J. Pullback and forward attractors for a damped wave equation with delays. (English) Zbl 1061.35153 Stoch. Dyn. 4, No. 3, 405-423 (2004). Reviewer: Wei Nian Li (Shanghai) MSC: 35R10 35Q53 35B41 47H20 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stoch. Dyn. 4, No. 3, 405--423 (2004; Zbl 1061.35153) Full Text: DOI
Caraballo, Tomás; Garrido-Atienza, María J.; Real, José Stochastic stabilization of differential systems with general decay rate. (English) Zbl 1157.93537 Syst. Control Lett. 48, No. 5, 397-406 (2003). MSC: 93E15 93D15 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Syst. Control Lett. 48, No. 5, 397--406 (2003; Zbl 1157.93537) Full Text: DOI
Caraballo, Tomás; Real, José Asymptotic behaviour of two-dimensional Navier-Stokes equations with delays. (English) Zbl 1057.35027 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 459, No. 2040, 3181-3194 (2003). Reviewer: Bruno Scarpellini (Basel) MSC: 35Q30 35R10 35B40 76D05 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{J. Real}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 459, No. 2040, 3181--3194 (2003; Zbl 1057.35027) Full Text: DOI
Caraballo, Tomás; Garrido-Atienza, María J.; Real, José The exponential behaviour of nonlinear stochastic functional equations of second order in time. (English) Zbl 1056.60058 Stoch. Dyn. 3, No. 2, 169-186 (2003). Reviewer: Evelyn Buckwar (Berlin) MSC: 60H15 35R60 35R10 35B40 93D20 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stoch. Dyn. 3, No. 2, 169--186 (2003; Zbl 1056.60058) Full Text: DOI
Caraballo, Tomás; Garrido-Atienza, María J.; Real, José Asymptotic stability of nonlinear stochastic evolution equations. (English) Zbl 1055.60065 Stochastic Anal. Appl. 21, No. 2, 301-327 (2003). Reviewer: Evelyn Buckwar (Berlin) MSC: 60H15 35R60 37L55 93D05 93D20 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stochastic Anal. Appl. 21, No. 2, 301--327 (2003; Zbl 1055.60065) Full Text: DOI
Caraballo, Tomás; Garrido-Atienza, María J.; Real, José Existence and uniqueness of solutions for delay stochastic evolution equations. (English) Zbl 1028.60056 Stochastic Anal. Appl. 20, No. 6, 1225-1256 (2002). Reviewer: Markus Riedle (Berlin) MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stochastic Anal. Appl. 20, No. 6, 1225--1256 (2002; Zbl 1028.60056) Full Text: DOI
Caraballo, Tomás; Real, José Navier-Stokes equations with delays. (English) Zbl 1007.35062 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 457, No. 2014, 2441-2453 (2001). Reviewer: Oleg Titow (Berlin) MSC: 35Q30 76D03 76D55 49J25 76D05 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{J. Real}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 457, No. 2014, 2441--2453 (2001; Zbl 1007.35062) Full Text: DOI Link
Caraballo, Tomás; Real, José On the pathwise exponential stability of nonlinear stochastic partial differential equations. (English) Zbl 0808.93069 Stochastic Anal. Appl. 12, No. 5, 517-525 (1994). MSC: 93E15 93C20 93D20 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{J. Real}, Stochastic Anal. Appl. 12, No. 5, 517--525 (1994; Zbl 0808.93069) Full Text: DOI Link
Caraballo, Tomás; Real, José Partial differential equations with delayed random perturbations: Existence, uniqueness, and stability of solutions. (English) Zbl 0790.60054 Stochastic Anal. Appl. 11, No. 5, 497-511 (1993). MSC: 60H15 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{J. Real}, Stochastic Anal. Appl. 11, No. 5, 497--511 (1993; Zbl 0790.60054) Full Text: DOI