Research Group Stochastic Analysis  of Differential Systems (aesdif)

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Prof. José A. Langa's Homepage

Research papers

(please feel free to ask for a copy of any of the documents listed below)

I. ATTRACTORS FOR RANDOM DYNAMICAL SYSTEMS

· T. Caraballo, J.A. Langa & J. C. Robinson, Upper semicontinuity of attractors for small random perturbations of dynamical systems, Commun. Part. Diff. Eq. 23 (1998), 1557-1581.

· F. Flandoli,  J.A. Langa, Determining modes for dissipative random dynamical systems, Stoch. and Stoch. Reports  66 (1999), 1-25.

· T. Caraballo & J.A. Langa, Tracking properties of trajectories on random attracting sets, Stoch. Anal. Appl. 17(3) (1999), 339-358.

· T. Caraballo, J.A. Langa & J. C. Robinson, Stability and random attractors for a reaction-diffusion equation with multiplicative noise, Discrete and Continuous Dynamical Systems-A 6 (4) (2000), 875-892.

· T. Caraballo, J.A. Langa & J. C. Robinson, A stochastic pitchfork bifurcation in a reaction-diffusion equation, Proc. R. Soc. Lond. A 457(2001), 2041-2061.

· T. Caraballo & J.A. Langa, On the theory of random attractors and some open problems, Proceedings of the Conference on Stochastic Partial Differential Equations and Applications, G. Da Prato and L. Tubaro (eds.), Pitman, Italy, LN Pure and Appl. Maths No. 227, 89-104, 2002. 

· J.A. Langa: Finite-dimensional limiting dynamics of random dynamical systems. Dyn. Syst. 18 (2003), no. 1, 57--68.

· H. Allouba, J.A. Langa: Semimartingale attractors for generalized Allen-Cahn SPDEs driven by space-time white noise. C. R. Math. Acad. Sci. Paris 337 (2003), no. 3, 201--206.

· H. Allouba, J.A. Langa: Semimartingale attractors for Allen-Cahn SPDEs driven by space-time white noise: Existence and finite dimensional asymptotic behaviour, Stoch. Dyn. 4 (2004), no. 2, 223--244.

· P.E. Kloeden, J.A. Langa: Flattening, squeezing and the existence of random attractors, Proc. Royal. Soc. London Ser. A, 463 (2007), 163—181.

· J.A. Langa, J.C. Robinson: Fractal dimension of a random invariant set. J. Math. Pures Appl. (9) 85 (2006), no. 2, 269—294.

II. NON-AUTONOMOUS DYNAMICAL SYSTEMS AND ATTRACTORS

· J.A. Langa, J.C. Robinson, A finite number of point observations which determine a non-autonomous fluid flow, Nonlinearity 14 (2001), 673-682.

· J.A. Langa, Asymptotically finite dimensional pullback behaviour of non autonomous PDEs, Ark. Math. 80 (5) (2003), 525-535.

· T. Caraballo & J.A. Langa, On the upper semicontinuity of cocycle attractors for nonautonomous and random dynamical systems, Dynamics of Continuous, Discrete and Impulsive Systems 10 (4) (2003), 491-513.

· T. Caraballo, P.E. Kloeden & J.A. Langa, Atractores globales para sistemas diferenciales no autónomos, CUBO 5 (2) (2003), 301-329.

· Caraballo, T., Langa, J.A., Valero, Dimension of attractors of non autonomous reaction-diffusion equations, ANZIAM 45 (2003), 207-222.

· J.A. Langa, B. Schmalfuss: Finite dimensionality of attractors for non-autonomous dynamical systems given by partial differential equations, Stoch. Dyn. 4 (2004), no. 3, 385--404.

· J.A. Langa, G. Łukaszewicz, J. Real: Finite fractal dimension of pullback attractors for non-autonomous 2D Navier–Stokes equations in some unbounded domains. Nonlinear Anal. 66 (3) (2007), 735—749.

· J.A. Langa, J.C. Robinson, A. Suárez: Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system. Nonlinearity 16 (2003), no. 4, 1277--1293.

· P.E. Kloeden; J.A. Langa, J. Real: Pullback $V$-attractors of the 3-dimensional globally modified Navier-Stokes equations. Commun. Pure Appl. Anal. 6 (2007), no. 4, 937--955.

· J.A. Langa.; J.C. Robinson; A. Rodríguez-Bernal.; A. Suárez.; A. Vidal-López: Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations. Discrete Contin. Dyn. Syst. 18 (2007), no. 2-3, 483--497.

III. GEOMETRICAL STRUCTURE OF GLOBAL ATTRACTORS

· A. Carvalho, J.A. Langa: Non-autonomous perturbation of autonomous semilinear differential equations: Continuity of local stable and unstable manifolds, J. Differential Equations 233 (2) (2007), 622-653.

· J.A. Langa, J.C. Robinson, A. Suárez, A. Vidal: The stability of attractors for non-autonomous perturbations of gradient-like systems, J. Differential Equations 234 (2) (2007), 607—625.

· A. Carvalho, J.A. Langa, J.C. Robinson, A. Suárez: Characterization of Non-Autonomous Attractors in Perturbed Infinite-Dimensional Gradient Systems, J. Differential Equations, 236 (2007), no. 2, 570--603.

· A. Carvalho, J.A. Langa, J.C. Robinson: Lower-semicontinuity of attractors for non-autonomous dynamical systems, Ergodic Theory of Dynamical Systems (2009).

· J.A. Langa, J.C. Robinson, A. Rodríguez-Bernal, A. Suárez: Permanence and asymptotically stable complete trajectories for non-autonomous Lotka-Volterra models with diffusion, SIAM Journal. of Anal. Math. (2009).

IV. STOCHASTIC ANALYSIS OF DIFFERENTIAL EQUATIONS

· T. Caraballo & J.A. Langa, Comparison of the long-time behaviour of linear Ito and Stratonovich partial differential equations, Stoch. Anal. Appl. 19(2) (2001), 183-195.

· T. Caraballo, J.A. Langa & T. Taniguchi, The exponential behaviour and stabilizability of stochastic 2D-Navier-Stokes equations, J. Differential Equations. 179 (2) (2002), 714-737.

· T. Caraballo, J.A. Langa, J. Valero: On the relationship between solutions of stochastic and random differential inclusions. Stochastic Anal. Appl. 21 (2003), no. 3, 545--557.

· T. Caraballo, I.D. Chueshov, J.A. Langa: Existence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equations. Nonlinearity 18 (2005), no. 2, 747--767.

· T. Caraballo, H. Crauel, J.A. Langa & J. C. Robinson: The effect of noise on the Chafee-Infante equation: a nonlinear case study. Proc. Amer. Math. Soc. 135 (2007), no. 2, 373—382.

· F. Flandoli; J.A. Langa: Markov attractors: a probabilistic approach to multivalued flows. Stoch. Dyn. 8 (2008), no. 1, 59--75.

IV. BIFURCATION IN NON-AUTONOMOUS DIFFERENTIAL EQUATIONS

· J.A. Langa, J.C. Robinson, A. Suárez: Non-autonomous bifurcation phenomena: Stability, instability, and bifurcation phenomena in non-autonomous differential equation, Nonlinearity 15(2002), no. 3, 887-903.

· J.A. Langa, A. Suárez: Bifurcation phenomena for a non autonomous logistic equation, Electronic J. Diff. Eqns. Vol. 2 (2002), no. 72, pp. 1-20. 

· J.A. Langa, J.C. Robinson, A. Suárez: Bifurcation from zero of a complete trajectory for nonautonomous logistic PDEs. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 15 (2005), no. 8, 2663--2669.

· J.A. Langa, J.C. Robinson, A. Suárez: Bifurcations in non-autonomous scalar equations, J. Differential Equations 221 (2006), no. 1, 1--35.

V. MULTIVALUED DYNAMICAL SYSTEMS

· T. Caraballo, J.A. Langa & J. Valero, Global attractors for multivalued random semiflows generated by random differential inclusions with additive noise, C.R. Acad. Sci. Paris, t. 332, Serie I (2001), 131-136.

· T. Caraballo, J.A. Langa & J. Valero, Global attractors for multivalued random dynamical systems generated by random differential inclusions with multiplicative noise, J. Math. Anal. Appl. 260 (2001), 602-622.

· T. Caraballo, J.A. Langa & J. Valero, Global attractors for multivalued random dynamical systems, Nonlinear Analysis TMA, 48 (6) (2002), 805-829.

· T. Caraballo, J.A. Langa & J. Valero, Approximations of attractors for multivalued random dynamical systems, International Journal of Mathematics, Game Theory and Algebra, 11 (4) (2001), 67-92.

· T. Caraballo, J.A. Langa, V. Melnik, J. Valero, Pullback attractors of nonautonomous and stochastic multivalued dynamical systems, Set Valued Analysis 11 (2) (2003), 153-201.

· T. Caraballo, J.A. Langa, J. Valero: Addendum to: "Global attractors for multivalued random dynamical systems" [Nonlinear Anal. 48 (2002), no. 6, Ser. A: Theory Methods, 805--829; MR1878338]. Nonlinear Anal. 61 (2005), no. 1-2, 277—279.

· T. Caraballo, J.A. Langa, J. Valero: Asymptotic behaviour of monotone multi-valued dynamical systems. Dyn. Syst. 20 (2005), no. 3, 301--321.

· T. Caraballo, J.A. Langa, J. Valero: Stabilisation of differential inclusions and PDEs without uniqueness by noise. Commun. Pure Appl. Anal. 7 (2008), no. 6, 1375--1392.

VI. QUALITATIVE BEHAVIOUR OF PARTIAL DIFFERENTIAL EQUATIONS

· J.A. Langa, J.C. Robinson, Determining asymptotic behaviour from the dynamics on attracting sets, J. Dynam. Diff. Equations.  11 (1999), 319-331.

· T. Caraballo, J.A. Langa & J. C. Robinson, Attractors for differential equations with variable delays, J. Math. Anal. Appl. 260 (2001), 421-438.

· J.A. Langa, J. C. Robinson, A. Suárez: Permanence in the non-autonomous Lotka-Volterra competition model, J. Differential Equations, 190 (2003), no. 1, 214--238.

· J.A. Langa, J. Real, J. Simon: Existence and Regularity of the Pressure for the Stochastic Navier–Stokes Equations, Applied Math. And Optimization 48 (3) (2003), 95-110.

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