Zhang, Qiangheng; Caraballo, Tomás; Yang, Shuang Stability of regular attractors for non-autonomous random dynamical systems and applications to stochastic Newton-Boussinesq equations with delays. (English) Zbl 07808495 Physica D 458, Article ID 134012, 10 p. (2024). MSC: 37L30 37L55 35B41 35R60 PDFBibTeX XMLCite \textit{Q. Zhang} et al., Physica D 458, Article ID 134012, 10 p. (2024; Zbl 07808495) Full Text: DOI
Wang, Renhai; Caraballo, Tomás; Tuan, Nguyen Huy Mean attractors and invariant measures of locally monotone and generally coercive SPDEs driven by superlinear noise. (English) Zbl 07781622 J. Differ. Equations 381, 209-259 (2024). MSC: 35B41 35B40 35R60 37L30 PDFBibTeX XMLCite \textit{R. Wang} et al., J. Differ. Equations 381, 209--259 (2024; Zbl 07781622) Full Text: DOI
Yang, Shuang; Li, Yangrong; Zhang, Qiangheng; Caraballo, Tomás Stability analysis of stochastic 3D Lagrangian-averaged Navier-Stokes equations with infinite delay. (English) Zbl 07781532 J. Dyn. Differ. Equations 35, No. 4, 3011-3054 (2023). MSC: 35Q30 35B40 35B35 35A01 35A02 35R07 35R60 PDFBibTeX XMLCite \textit{S. Yang} et al., J. Dyn. Differ. Equations 35, No. 4, 3011--3054 (2023; Zbl 07781532) Full Text: DOI
Caraballo, Tomás; Chen, Zhang; Yang, Dandan Random dynamics and limiting behaviors for 3D globally modified Navier-Stokes equations driven by colored noise. (English) Zbl 07778799 Stud. Appl. Math. 151, No. 1, 247-284 (2023). MSC: 37L55 37L40 37L30 35Q35 35Q30 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stud. Appl. Math. 151, No. 1, 247--284 (2023; Zbl 07778799) Full Text: DOI
Wang, Fengling; Caraballo, Tomás; Li, Yangrong Dynamics of multi-valued retarded \(p\)-Laplace equations driven by nonlinear colored noise. (English) Zbl 07775744 J. Math. Phys. 64, No. 10, Article ID 102701, 29 p. (2023). MSC: 35L55 35L30 35B41 35J92 PDFBibTeX XMLCite \textit{F. Wang} et al., J. Math. Phys. 64, No. 10, Article ID 102701, 29 p. (2023; Zbl 07775744) Full Text: DOI
Li, Lingyu; Chen, Zhang; Caraballo, Tomás Dynamics of a stochastic fractional nonlocal reaction-diffusion model driven by additive noise. (English) Zbl 1526.60039 Discrete Contin. Dyn. Syst., Ser. S 16, No. 10, 2530-2558 (2023). MSC: 60H15 35B40 35B41 35R60 35R11 35K57 37A50 PDFBibTeX XMLCite \textit{L. Li} et al., Discrete Contin. Dyn. Syst., Ser. S 16, No. 10, 2530--2558 (2023; Zbl 1526.60039) Full Text: DOI
Wang, Fengling; Caraballo, Tomás; Li, Yangrong; Wang, Renhai Periodic measures for the stochastic delay modified Swift-Hohenberg lattice systems. (English) Zbl 1526.37086 Commun. Nonlinear Sci. Numer. Simul. 125, Article ID 107341, 26 p. (2023). MSC: 37L60 37L55 37L40 60H10 PDFBibTeX XMLCite \textit{F. Wang} et al., Commun. Nonlinear Sci. Numer. Simul. 125, Article ID 107341, 26 p. (2023; Zbl 1526.37086) Full Text: DOI
Tuan, Nguyen Huy; Caraballo, Tomás; Thach, Tran Ngoc New results for stochastic fractional pseudo-parabolic equations with delays driven by fractional Brownian motion. (English) Zbl 07697538 Stochastic Processes Appl. 161, 24-67 (2023). MSC: 60H15 35K70 60G22 60H10 PDFBibTeX XMLCite \textit{N. H. Tuan} et al., Stochastic Processes Appl. 161, 24--67 (2023; Zbl 07697538) Full Text: DOI
Xu, Jiaohui; Caraballo, Tomás Dynamics of stochastic nonlocal reaction-diffusion equations driven by multiplicative noise. (English) Zbl 1512.35113 Anal. Appl., Singap. 21, No. 3, 597-633 (2023). MSC: 35B41 35K20 35K57 35R60 37L30 PDFBibTeX XMLCite \textit{J. Xu} and \textit{T. Caraballo}, Anal. Appl., Singap. 21, No. 3, 597--633 (2023; Zbl 1512.35113) Full Text: DOI
Li, Yangrong; Yang, Shuang; Caraballo, Tomás Optimization and convergence of numerical attractors for discrete-time quasi-linear lattice system. (English) Zbl 1512.65161 SIAM J. Numer. Anal. 61, No. 2, 905-928 (2023). MSC: 65L20 35B40 37L60 PDFBibTeX XMLCite \textit{Y. Li} et al., SIAM J. Numer. Anal. 61, No. 2, 905--928 (2023; Zbl 1512.65161) Full Text: DOI
Wang, Renhai; Caraballo, Tomás; Tuan, Nguyen Huy Asymptotic stability of evolution systems of probability measures for nonautonomous stochastic systems: theoretical results and applications. (English) Zbl 1528.37067 Proc. Am. Math. Soc. 151, No. 6, 2449-2458 (2023). MSC: 37L55 37L60 37L30 37L40 35B40 35B41 60H15 PDFBibTeX XMLCite \textit{R. Wang} et al., Proc. Am. Math. Soc. 151, No. 6, 2449--2458 (2023; Zbl 1528.37067) Full Text: DOI arXiv
Caraballo, Tomás; Tuan, Nguyen Huy New results for convergence problem of fractional diffusion equations when order approach to \(1^-\). (English) Zbl 1524.35025 Differ. Integral Equ. 36, No. 5-6, 491-516 (2023). Reviewer: Vincenzo Vespri (Firenze) MSC: 35A08 26A33 35B65 35R11 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{N. H. Tuan}, Differ. Integral Equ. 36, No. 5--6, 491--516 (2023; Zbl 1524.35025) Full Text: DOI
Zhao, Caidi; Jiang, Huite; Li, Chunqiu; Caraballo, Tomás Statistical solutions and its limiting behavior for the impulsive discrete Ginzburg-Landau equations. (Chinese. English summary) Zbl 1524.35092 Acta Math. Sci., Ser. A, Chin. Ed. 42, No. 3, 784-806 (2022). MSC: 35B41 34D35 76F20 PDFBibTeX XMLCite \textit{C. Zhao} et al., Acta Math. Sci., Ser. A, Chin. Ed. 42, No. 3, 784--806 (2022; Zbl 1524.35092) Full Text: Link
Caraballo, Tomás; Langa, José A.; Carvalho, Alexandre N.; Oliveira-Sousa, Alexandre N. Continuity and topological structural stability for nonautonomous random attractors. (English) Zbl 1507.35352 Stoch. Dyn. 22, No. 7, Article ID 2240024, 28 p. (2022). MSC: 35R60 35B41 35L71 37L55 37B35 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stoch. Dyn. 22, No. 7, Article ID 2240024, 28 p. (2022; Zbl 1507.35352) Full Text: DOI arXiv
Liu, Yarong; Wang, Yejuan; Caraballo, Tomas Nontrivial equilibrium solutions and general stability for stochastic evolution equations with pantograph delay and tempered fractional noise. (English) Zbl 1500.60038 SIAM J. Math. Anal. 54, No. 5, 5629-5661 (2022). MSC: 60H15 35A02 35B35 60G22 PDFBibTeX XMLCite \textit{Y. Liu} et al., SIAM J. Math. Anal. 54, No. 5, 5629--5661 (2022; Zbl 1500.60038) Full Text: DOI
Yang, Dandan; Chen, Zhang; Caraballo, Tomás Dynamics of a globally modified Navier-Stokes model with double delay. (English) Zbl 1498.35448 Z. Angew. Math. Phys. 73, No. 5, Paper No. 216, 32 p. (2022). MSC: 35Q35 35Q30 35B40 37L30 76D05 35R07 35R06 PDFBibTeX XMLCite \textit{D. Yang} et al., Z. Angew. Math. Phys. 73, No. 5, Paper No. 216, 32 p. (2022; Zbl 1498.35448) Full Text: DOI
Liu, Yarong; Wang, Yejuan; Caraballo, Tomás The continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise. (English) Zbl 1500.35318 Stoch. Dyn. 22, No. 5, Article ID 2250022, 50 p. (2022). Reviewer: Lucio Galeati (Lausanne) MSC: 35R60 35B30 35B35 35B65 35Q35 60H15 PDFBibTeX XMLCite \textit{Y. Liu} et al., Stoch. Dyn. 22, No. 5, Article ID 2250022, 50 p. (2022; Zbl 1500.35318) Full Text: DOI
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
Wang, Jingyu; Wang, Yejuan; Yang, Lin; Caraballo, Tomás Random attractors for stochastic delay wave equations on \(\mathbb{R}^n\) with linear memory and nonlinear damping. (English) Zbl 1498.35104 Discrete Contin. Dyn. Syst., Ser. S 15, No. 10, 3025-3057 (2022). MSC: 35B41 35L15 35R09 35R60 37L55 PDFBibTeX XMLCite \textit{J. Wang} et al., Discrete Contin. Dyn. Syst., Ser. S 15, No. 10, 3025--3057 (2022; Zbl 1498.35104) Full Text: DOI
Wang, Jingyu; Wang, Yejuan; Caraballo, Tomás Multi-valued random dynamics of stochastic wave equations with infinite delays. (English) Zbl 1496.35093 Discrete Contin. Dyn. Syst., Ser. B 27, No. 10, 6147-6172 (2022). MSC: 35B40 35L20 35R09 35R10 37L30 37L55 PDFBibTeX XMLCite \textit{J. Wang} et al., Discrete Contin. Dyn. Syst., Ser. B 27, No. 10, 6147--6172 (2022; Zbl 1496.35093) Full Text: DOI
Nguyen, Anh Tuan; Caraballo, Tomás; Tuan, Nguyen Huy On the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivative. (English) Zbl 1501.35443 Proc. R. Soc. Edinb., Sect. A, Math. 152, No. 4, 989-1031 (2022). Reviewer: Ismail Huseynov (Mersin) MSC: 35R11 26A33 33E12 35B40 35K30 35K58 PDFBibTeX XMLCite \textit{A. T. Nguyen} et al., Proc. R. Soc. Edinb., Sect. A, Math. 152, No. 4, 989--1031 (2022; Zbl 1501.35443) Full Text: DOI arXiv
Caraballo, Tomás; López-de-la-Cruz, Javier; Rapaport, Alain Study of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuations. (English) Zbl 1501.34041 Stoch. Dyn. 22, No. 3, Article ID 2240002, 22 p. (2022). MSC: 34C60 92D25 34F05 34D05 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stoch. Dyn. 22, No. 3, Article ID 2240002, 22 p. (2022; Zbl 1501.34041) Full Text: DOI
Caraballo, Tomás; Ngoc, Tran Bao; Thach, Tran Ngoc; Tuan, Nguyen Huy On a stochastic nonclassical diffusion equation with standard and fractional Brownian motion. (English) Zbl 1491.35469 Stoch. Dyn. 22, No. 2, Article ID 2140011, 45 p. (2022). MSC: 35R60 35B65 35K20 35R11 26A33 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stoch. Dyn. 22, No. 2, Article ID 2140011, 45 p. (2022; Zbl 1491.35469) 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
Caraballo, Tomás; López-de-la-Cruz, Javier Bounded random fluctuations on the input flow in chemostat models with wall growth and non-monotonic kinetics. (English) Zbl 1525.34089 AIMS Math. 6, No. 4, 4025-4052 (2021). MSC: 34F05 92D25 92D40 60H10 34C60 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{J. López-de-la-Cruz}, AIMS Math. 6, No. 4, 4025--4052 (2021; Zbl 1525.34089) Full Text: DOI
Caraballo, Tomás; Guo, Boling; Tuan, Nguyen Huy; Wang, Renhai Asymptotically autonomous robustness of random attractors for a class of weakly dissipative stochastic wave equations on unbounded domains. (English) Zbl 1491.37067 Proc. R. Soc. Edinb., Sect. A, Math. 151, No. 6, 1700-1730 (2021). Reviewer: Bixiang Wang (Socorro) MSC: 37L55 37L30 35R60 35B41 35B40 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Proc. R. Soc. Edinb., Sect. A, Math. 151, No. 6, 1700--1730 (2021; Zbl 1491.37067) Full Text: DOI
Zhao, Caidi; Jiang, Huite; Caraballo, Tomás Statistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on infinite lattices. (English) Zbl 1510.35158 Appl. Math. Comput. 404, Article ID 126103, 14 p. (2021). MSC: 35K57 34A33 34A37 34D35 35B41 37L60 PDFBibTeX XMLCite \textit{C. Zhao} et al., Appl. Math. Comput. 404, Article ID 126103, 14 p. (2021; Zbl 1510.35158) Full Text: DOI
Wang, Yejuan; Liu, Yarong; Caraballo, Tomás Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions. (English) Zbl 1470.35070 J. Evol. Equ. 21, No. 2, 1779-1807 (2021). MSC: 35B40 35R60 35R10 PDFBibTeX XMLCite \textit{Y. Wang} et al., J. Evol. Equ. 21, No. 2, 1779--1807 (2021; Zbl 1470.35070) Full Text: DOI Link
Caraballo, Tomás; Ngoc, Tran Bao; Tuan, Nguyen Huy; Wang, Renhai On a nonlinear Volterra integrodifferential equation involving fractional derivative with Mittag-Leffler kernel. (English) Zbl 1466.35355 Proc. Am. Math. Soc. 149, No. 8, 3317-3334 (2021). MSC: 35R11 35R09 26A33 35B65 35B05 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Proc. Am. Math. Soc. 149, No. 8, 3317--3334 (2021; Zbl 1466.35355) Full Text: DOI
Caraballo, Tomás; Carvalho, Alexandre N.; Langa, José A.; Oliveira-Sousa, Alexandre N. The effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equations. (English) Zbl 1465.37065 J. Math. Anal. Appl. 500, No. 2, Article ID 125134, 27 p. (2021). MSC: 37H30 37L55 37L15 37L45 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Math. Anal. Appl. 500, No. 2, Article ID 125134, 27 p. (2021; Zbl 1465.37065) Full Text: DOI arXiv Link
Xu, Jiaohui; Zhang, Zhengce; Caraballo, Tomás Non-autonomous nonlocal partial differential equations with delay and memory. (English) Zbl 1451.35072 J. Differ. Equations 270, 505-546 (2021). MSC: 35K58 35K20 35R10 35B41 PDFBibTeX XMLCite \textit{J. Xu} et al., J. Differ. Equations 270, 505--546 (2021; Zbl 1451.35072) Full Text: DOI Link
Caraballo, Tomás; Colucci, Renato; López-de-la-Cruz, Javier; Rapaport, Alain Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate. (English) Zbl 1471.92215 Math. Biosci. Eng. 17, No. 6, 7480-7501 (2020). MSC: 92C75 60J60 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Math. Biosci. Eng. 17, No. 6, 7480--7501 (2020; Zbl 1471.92215) Full Text: DOI
Wang, Yejuan; Caraballo, Tomás Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems. (English) Zbl 1453.37019 Discrete Contin. Dyn. Syst., Ser. S 13, No. 8, 2303-2326 (2020). MSC: 37B35 37B30 PDFBibTeX XMLCite \textit{Y. Wang} and \textit{T. Caraballo}, Discrete Contin. Dyn. Syst., Ser. S 13, No. 8, 2303--2326 (2020; Zbl 1453.37019) Full Text: DOI
Caraballo, Tomás; Colucci, Renato; López-de-la-Cruz, Javier; Rapaport, Alain A way to model stochastic perturbations in population dynamics models with bounded realizations. (English) Zbl 1485.92080 Commun. Nonlinear Sci. Numer. Simul. 77, 239-257 (2019); corrigendum ibid. 96, Article ID 105681, 5 p. (2021). Reviewer: Shi-Liang Wu (Xi’an) MSC: 92D25 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Commun. Nonlinear Sci. Numer. Simul. 77, 239--257 (2019; Zbl 1485.92080) Full Text: DOI HAL
Liu, Linfang; Caraballo, Tomás Analysis of a stochastic \(2D\)-Navier-Stokes model with infinite delay. (English) Zbl 1427.35182 J. Dyn. Differ. Equations 31, No. 4, 2249-2274 (2019). MSC: 35Q30 35R60 35B40 35A01 35A02 35D30 35B35 76D03 76D05 PDFBibTeX XMLCite \textit{L. Liu} and \textit{T. Caraballo}, J. Dyn. Differ. Equations 31, No. 4, 2249--2274 (2019; Zbl 1427.35182) Full Text: DOI
Caraballo, Tomás; Keraani, Sami Analysis of a stochastic SIR model with fractional Brownian motion. (English) Zbl 1407.92125 Stochastic Anal. Appl. 36, No. 5, 895-908 (2018). MSC: 92D30 60H10 34D20 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{S. Keraani}, Stochastic Anal. Appl. 36, No. 5, 895--908 (2018; Zbl 1407.92125) Full Text: DOI Link
Caraballo, Tomás; Herrera-Cobos, Marta; Marín-Rubio, Pedro Robustness of time-dependent attractors in \(H^1\)-norm for nonlocal problems. (English) Zbl 1415.35056 Discrete Contin. Dyn. Syst., Ser. B 23, No. 3, 1011-1036 (2018). Reviewer: Bixiang Wang (Socorro) MSC: 35B41 35B65 35K57 35Q92 37L30 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Discrete Contin. Dyn. Syst., Ser. B 23, No. 3, 1011--1036 (2018; Zbl 1415.35056) Full Text: DOI
Liu, Linfang; Caraballo, Tomás; Kloeden, Peter Long time behavior of stochastic parabolic problems with white noise in materials with thermal memory. (English) Zbl 1377.35296 Rev. Mat. Complut. 30, No. 3, 687-717 (2017). MSC: 35R60 35B40 35K20 37H10 60H15 PDFBibTeX XMLCite \textit{L. Liu} et al., Rev. Mat. Complut. 30, No. 3, 687--717 (2017; Zbl 1377.35296) Full Text: DOI Link
Caraballo, Tomás; Garrido-Atienza, María J.; López-de-la-Cruz, J. Dynamics of some stochastic chemostat models with multiplicative noise. (English) Zbl 1367.34056 Commun. Pure Appl. Anal. 16, No. 5, 1893-1914 (2017). MSC: 34C60 34F05 60H10 92D25 34D45 34D05 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Commun. Pure Appl. Anal. 16, No. 5, 1893--1914 (2017; Zbl 1367.34056) Full Text: DOI
Rivero, Felipe; Márquez-Durán, Antonio M.; Caraballo, Tomás Asymptotic behaviour of a non-classical and non-autonomous diffusion equation containing some hereditary characteristic. (English) Zbl 1366.35233 Discrete Contin. Dyn. Syst., Ser. B 22, No. 5, 1817-1833 (2017). MSC: 35R15 35B41 37B55 47J35 PDFBibTeX XMLCite \textit{F. Rivero} et al., Discrete Contin. Dyn. Syst., Ser. B 22, No. 5, 1817--1833 (2017; Zbl 1366.35233) 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
Caraballo, Tomás; Colucci, Renato Stabilization of oscillations in a phase transition model. (English) Zbl 1357.60066 Math. Methods Appl. Sci. 40, No. 3, 823-832 (2017). MSC: 60H15 60H30 35R60 74N15 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{R. Colucci}, Math. Methods Appl. Sci. 40, No. 3, 823--832 (2017; Zbl 1357.60066) Full Text: DOI Link
Caraballo, T.; Langa, J. A.; Obaya, R. Pullback, forward and chaotic dynamics in 1D non-autonomous linear-dissipative equations. (English) Zbl 1375.37106 Nonlinearity 30, No. 1, 274-299 (2017). Reviewer: David Cheban (Chisinau) MSC: 37D45 37A20 37C60 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Nonlinearity 30, No. 1, 274--299 (2017; Zbl 1375.37106) Full Text: DOI Link
Bonotto, E. M.; Bortolan, M. C.; Caraballo, T.; Collegari, R. Attractors for impulsive non-autonomous dynamical systems and their relations. (English) Zbl 1362.35326 J. Differ. Equations 262, No. 6, 3524-3550 (2017). MSC: 35R12 35B41 34A37 PDFBibTeX XMLCite \textit{E. M. Bonotto} et al., J. Differ. Equations 262, No. 6, 3524--3550 (2017; Zbl 1362.35326) Full Text: DOI Link
Caraballo, Tomás; Colucci, Renato A comparison between random and stochastic modeling for a SIR model. (English) Zbl 1367.34055 Commun. Pure Appl. Anal. 16, No. 1, 151-162 (2017). Reviewer: Alexandra Rodkina (Kingston/Jamaica) MSC: 34C60 34F05 60H10 92D30 34D45 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{R. Colucci}, Commun. Pure Appl. Anal. 16, No. 1, 151--162 (2017; Zbl 1367.34055) Full Text: DOI
Caraballo, Tomás; Garrido-Atienza, María J.; López-de-la-Cruz, Javier Some aspects concerning the dynamics of stochastic chemostats. (English) Zbl 1360.92075 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, 227-246 (2016). MSC: 92C99 60J70 60H40 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stud. Syst. Decis. Control 69, 227--246 (2016; Zbl 1360.92075) Full Text: DOI Link
Asai, Yusuke; Caraballo, Tomás; Han, Xiaoying; Kloeden, Peter E. A random model for immune response to virus in fluctuating environments. (English) Zbl 1360.92067 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, 211-225 (2016). MSC: 92C60 92D30 60H10 PDFBibTeX XMLCite \textit{Y. Asai} et al., Stud. Syst. Decis. Control 69, 211--225 (2016; Zbl 1360.92067) Full Text: DOI Link
Caraballo, Tomás; Colucci, Renato; Han, Xiaoying Predation with indirect effects in fluctuating environments. (English) Zbl 1354.37092 Nonlinear Dyn. 84, No. 1, 115-126 (2016). MSC: 37N25 92D25 37H10 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Nonlinear Dyn. 84, No. 1, 115--126 (2016; Zbl 1354.37092) Full Text: DOI Link
Caraballo, Tomás; Colucci, Renato; Han, Xiaoying Semi-Kolmogorov models for predation with indirect effects in random environments. (English) Zbl 1347.92060 Discrete Contin. Dyn. Syst., Ser. B 21, No. 7, 2129-2143 (2016). MSC: 92D25 34C60 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Discrete Contin. Dyn. Syst., Ser. B 21, No. 7, 2129--2143 (2016; Zbl 1347.92060) Full Text: DOI
Caraballo, Tomás; Hammami, Mohamed Ali; Mchiri, Lassaad On the practical global uniform asymptotic stability of stochastic differential equations. (English) Zbl 1337.60117 Stochastics 88, No. 1, 45-56 (2016). MSC: 60H10 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stochastics 88, No. 1, 45--56 (2016; Zbl 1337.60117) Full Text: DOI arXiv Link
Caraballo, Tomás; Han, Xiaoying; Schmalfuss, Björn; Valero, José Random attractors for stochastic lattice dynamical systems with infinite multiplicative white noise. (English) Zbl 1329.60208 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 130, 255-278 (2016). MSC: 60H15 37H10 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 130, 255--278 (2016; Zbl 1329.60208) Full Text: DOI Link
Caraballo, Tomás; Han, Xiaoying; Kloeden, Peter E. Chemostats with random inputs and wall growth. (English) Zbl 1341.34053 Math. Methods Appl. Sci. 38, No. 16, 3538-3550 (2015). Reviewer: Alexandra Rodkina (Kingston/Jamaica) MSC: 34C60 92D40 34F05 92D25 34D45 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Math. Methods Appl. Sci. 38, No. 16, 3538--3550 (2015; Zbl 1341.34053) Full Text: DOI Link
Caraballo, Tomás; Han, Xiaoying A survey on Navier-Stokes models with delays: existence, uniqueness and asymptotic behavior of solutions. (English) Zbl 1406.35221 Discrete Contin. Dyn. Syst., Ser. S 8, No. 6, 1079-1101 (2015). MSC: 35Q30 35-02 35A01 35A02 35B40 37H10 76D05 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{X. Han}, Discrete Contin. Dyn. Syst., Ser. S 8, No. 6, 1079--1101 (2015; Zbl 1406.35221) 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
Anguiano, María; Caraballo, Tomás Asymptotic behaviour of a non-autonomous Lorenz-84 system. (English) Zbl 1351.37075 Discrete Contin. Dyn. Syst. 34, No. 10, 3901-3920 (2014). MSC: 37B55 35B41 37L30 PDFBibTeX XMLCite \textit{M. Anguiano} and \textit{T. Caraballo}, Discrete Contin. Dyn. Syst. 34, No. 10, 3901--3920 (2014; Zbl 1351.37075) 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
Bortolan, M. C.; Caraballo, T.; Carvalho, A. N.; Langa, J. A. An estimate on the fractal dimension of attractors of gradient-like dynamical systems. (English) Zbl 1248.37020 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 14, 5702-5722 (2012). MSC: 37B25 28A80 28A78 37C45 PDFBibTeX XMLCite \textit{M. C. Bortolan} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 14, 5702--5722 (2012; Zbl 1248.37020) Full Text: DOI Link
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
Caraballo, Tomás; Cheban, David Levitan/Bohr almost periodic and almost automorphic solutions of second order monotone differential equations. (English) Zbl 1236.37017 J. Differ. Equations 251, No. 3, 708-727 (2011). Reviewer: Ubiratan D’Ambrosio (São Paulo) MSC: 37C10 34C27 34C11 37C55 37C70 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{D. Cheban}, J. Differ. Equations 251, No. 3, 708--727 (2011; Zbl 1236.37017) Full Text: DOI Link
Caraballo, T.; Garrido-Atienza, M. J.; Taniguchi, T. The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion. (English) Zbl 1218.60053 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 11, 3671-3684 (2011). MSC: 60H15 60G22 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 11, 3671--3684 (2011; Zbl 1218.60053) Full Text: DOI Link
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
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
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
Caraballo, Tomás; Carvalho, Alexandre N.; Langa, José A.; Rivero, Felipe Existence of pullback attractors for pullback asymptotically compact processes. (English) Zbl 1195.34086 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 3-4, 1967-1976 (2010). Reviewer: Zhenbin Fan (Jiangsu) MSC: 34G20 34D45 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 3--4, 1967--1976 (2010; Zbl 1195.34086) Full Text: DOI Link
Caraballo, Tomás; Lu, Kening Attractors for stochastic lattice dynamical systems with a multiplicative noise. (English) Zbl 1155.60324 Front. Math. China 3, No. 3, 317-335 (2008). MSC: 60H15 34B45 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{K. Lu}, Front. Math. China 3, No. 3, 317--335 (2008; Zbl 1155.60324) Full Text: DOI Link
Caraballo, Tomás; Kloeden, Peter E.; Neuenkirch, Andreas Synchronization of systems with multiplicative noise. (English) Zbl 1149.60036 Stoch. Dyn. 8, No. 1, 139-154 (2008). Reviewer: Henri Schurz (Carbondale) MSC: 60H10 34F05 37H10 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stoch. Dyn. 8, No. 1, 139--154 (2008; Zbl 1149.60036) 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
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, T.; Kloeden, P. E.; Marín-Rubio, P. Global and pullback attractors of set-valued skew product flows. (English) Zbl 1115.37065 Ann. Mat. Pura Appl. (4) 185, Suppl. 5, S23-S45 (2006). Reviewer: Norbert Koksch (Dresden) MSC: 37L30 34D45 37B25 34G25 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Ann. Mat. Pura Appl. (4) 185, S23--S45 (2006; Zbl 1115.37065) Full Text: DOI Link
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, Tomás; Kloeden, Peter E. The persistence of synchronization under environmental noise. (English) Zbl 1206.60054 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 461, No. 2059, 2257-2267 (2005). MSC: 60H10 34F05 37H10 PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{P. E. Kloeden}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 461, No. 2059, 2257--2267 (2005; Zbl 1206.60054) Full Text: DOI
Caraballo, T.; Marín-Rubio, P.; Valero, J. Autonomous and non-autonomous attractors for differential equations with delays. (English) Zbl 1074.34070 J. Differ. Equations 208, No. 1, 9-41 (2005). Reviewer: Ioannis P. Stavroulakis (Ioannina) MSC: 34K25 37C70 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Differ. Equations 208, No. 1, 9--41 (2005; Zbl 1074.34070) Full Text: DOI Link
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, 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
Caraballo, T.; Kloeden, P. E.; Marín-Rubio, P. Weak pullback attractors of setvalued processes. (English) Zbl 1044.93035 J. Math. Anal. Appl. 288, No. 2, 692-707 (2003). Reviewer: Marc Quincampoix (Brest) MSC: 93C30 34A60 37L30 49J53 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Math. Anal. Appl. 288, No. 2, 692--707 (2003; Zbl 1044.93035) Full Text: DOI Link
Caraballo, T.; Langa, J. A.; Valero, J. On the relationship between solutions of stochastic and random differential inclusions. (English) Zbl 1042.60037 Stochastic Anal. Appl. 21, No. 3, 545-557 (2003). MSC: 60H99 60H25 60H15 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Stochastic Anal. Appl. 21, No. 3, 545--557 (2003; Zbl 1042.60037) Full Text: DOI
Caraballo, T.; Langa, J. A.; Valero, J. Global attractors for multivalued random dynamical systems. (English) Zbl 1004.37035 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 48, No. 6, 805-829 (2002); addendum ibid. 61, No. 1-2, 277-279 (2005). Reviewer: Messoud Efendiev (Berlin) MSC: 37H10 60H15 34G25 35B41 35R70 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 48, No. 6, 805--829 (2002; Zbl 1004.37035) Full Text: DOI
Caraballo, Tomás; Langa, José A.; Robinson, James C. Attractors for differential equations with variable delays. (English) Zbl 0997.34073 J. Math. Anal. Appl. 260, No. 2, 421-438 (2001). Reviewer: Stieg Olof Londen (Espoo) MSC: 34K25 34D45 34K20 34K05 37C70 PDFBibTeX XMLCite \textit{T. Caraballo} et al., J. Math. Anal. Appl. 260, No. 2, 421--438 (2001; Zbl 0997.34073) Full Text: DOI
Caraballo, Tomás; Langa, José A.; Robinson, James C. Upper semicontinuity of attractors for small random perturbations of dynamical systems. (English) Zbl 0917.35169 Commun. Partial Differ. Equations 23, No. 9-10, 1557-1581 (1998). Reviewer: S.Méléard (Paris) MSC: 35R60 60H15 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Commun. Partial Differ. Equations 23, No. 9--10, 1557--1581 (1998; Zbl 0917.35169) Full Text: DOI