Caraballo Garrido, Tomás

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I got my degree and PhD at the Universidad de Sevilla, defending my PhD thesis in 1988 under the supervision of Prof. José Real Anguas, who was a world recognized expert in the field of stochastic partial differential equations.  

My first contributions focused on the local stability analysis and stabilization of several problems modeled by stochastic partial differential equations with hereditary properties (delays, memory, etc). Next, my interest focused on the new theory of random dynamical systems, where, jointly with my first PhD student, José A. Langa, we started to contribute. Almost at the same time, the theory of non-autonomous dynamical system started to experience new approaches, and new techniques were started to be developed for such systems: the pullback convergence concepts from the random theory. This justifies the beginning of our collaboration with Prof. Kloeden and his team, contributing in this way to the development of these theories which nowadays are still being analyzed intensively, but most importantly, is being applied to many problems in the Applied Sciences. It is worth mentioning that one of my papers on this topic, in which, we characterize the existence of pullback attractors, is one of the most cited papers according to ISI, and currently, I am amongst the first Spanish mathematicians according to the Highly cited scientists list elaborated by Thomson and Reuters.  

With the collaboration of Profesor Real, at the beginning of 2001, we consolidated a research group formed by researchers of the Universidad de Sevilla (called Stochastic Analysis of Differential Systems (AESDIF), with reference FQM-314, and we started a very fruitful collaboration amongst us and including many other recognized researchers in the field. As Principal Investigator, I have been awarded significant research projects, haver supervised 14 PhD and currently I am supervising 3 more, I have chaired several international conferences and numerous One-Day workshops. These activities ensure an important international activity. I have collaborated with more than 110 researchers, being worth mentioning Alexandre N. Carvalho (Universidade de Sao Paulo), David N. Cheban (University of Moldova), Igor D. Chueshov (V. Karazin Kharkov National University), Hans Crauel (Universität Goethe), Peter E. Kloeden (Universität Goethe), J.A. Langa (Universidad de Sevilla), G. Lukaszewicz (University of Warsaw), Rafael Obaya (Universidad de Valladolid), J. C. Robinson (University of Warwick), José Valero (Universidad Miguel Hernández), etc. 

As a consequence, I have been invited to deliver many plenary and main talks in international conferences, I have taken part in many scientific committees, I am member of several editorial committees of relevant journals and guest editor of many special issues. Moreover, I have been member of many PhD thesis committees and I have also been member of assessment committees for research projects, both at national and international level.  

Over the last years, my scientific interest focuses on the stochastic differential equations (ordinary and partial) with or without delays, the asymptotic behavior of dynamical systems  perturbed by noisy terms, multivalued dynamical systems, non-autonomous dynamical systems, and applications to models from the applied sciences (biology, ecology, epidemiology, etc). I have published more tan 250 research papers in top journals with high impact factor, 1 book, and I appear now in the list of 100.000 most influential researchers in the world. 

Main research results

  • Xu, Jiaohui; Zhang, Zhengce; Caraballo, Tomás; Non-autonomous nonlocal partial differential equations with delay and memory. J. Differential Equations 270 (2021), 505-546
  • Boukanjime, Brahim; Caraballo, Tomás; El Fatini, Mohamed; El Khalifi, Mohamed; Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching. Chaos Solitons Fractals 141 (2020), 110361. 
  • Wang, Jintao; Zhao, Caidi; Caraballo, Tomás; Invariant measures for the 3D globally modified Navier-Stokes equations with unbounded variable delays. Commun. Nonlinear Sci. Numer. Simul. 91 (2020), 105459. 
  • López-de-la-Cruz, Javier; Pérez-Aranda, María; Alcudia, Ana; Begines, Belén; Caraballo, Tomás; Pajuelo, Eloísa; Ginel, Pedro J.; Dynamics and numerical simulations to predict empirical antibiotic treatment of multi-resistant Pseudomonasaeruginosa infection. Commun. Nonlinear Sci. Numer. Simul. 91 (2020), 105418 
  • Caraballo, Tomás; Fatini, Mohamed El; Khalifi, Mohamed El; Gerlach, Richard; Pettersson, Roger; Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel. Chaos Solitons Fractals 133 (2020), 109643.
  • Sun, Wenlong; Caraballo, Tomás; Han, Xiaoying; Kloeden, Peter E.; A free boundary tumor model with time dependent nutritional supply. Nonlinear Anal. Real World Appl. 53 (2020), 103063
  • Liu, Linfang; Caraballo, Tomás; Kloeden, Peter E.; The asymptotic behaviour of fractional lattice systems with variable delay. Fract. Calc. Appl. Anal. 22 (2019), no. 3, 681–698.
  • Xu, Jiaohui; Zhang, Zhengce; Caraballo, Tomás; Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay. Commun. Nonlinear Sci. Numer. Simul. 75 (2019), 121–139. 
  • Caraballo, Tomás; Cortés, J.-C.; Navarro-Quiles, A.; Applying the random variable transformation method to solve a class of random linear differential equation with discrete delay. Appl. Math. Comput. 356 (2019), 198–218.
  • Bonotto, E. M.; Bortolan, M. C.; Caraballo, T.; Collegari, R.; Attractors for impulsive non-autonomous dynamical systems and their relations. J. Differential Equations 262 (2017), no. 6, 3524–3550.
  • Caraballo, Tomás; Han, Xiaoying; Schmalfuss, Björn; Valero, José; Random attractors for stochastic lattice dynamical systems with infinite multiplicative white noise. Nonlinear Anal. 130 (2016), 255–278.
  • Caraballo, Tomás; Han, Xiaoying; Kloeden, Peter E.; Nonautonomous Chemostats with Variable Delays. SIAM J. Math. Anal. 47 (2015), no. 3, 2178–2199.
  • Aragão-Costa, E. R.; Caraballo, T.; Carvalho, A. N.; Langa, J. A.; Non-autonomous Morse-decomposition and Lyapunov functions for gradient-like processes. Trans. Amer. Math. Soc. 365 (2013), no. 10, 5277–5312.
  • 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. Nonlinear Anal. 74 (2011), no. 11, 3671–3684
  • Caraballo, T.; Łukaszewicz, G.; Real, J. Pullback attractors for asymptotically compact non-autonomous dynamical systems. Nonlinear Anal. 64 (2006), no. 3, 484–498.
  • Caraballo, T.; Real, J. Attractors for 2D-Navier-Stokes models with delays. J. Differential Equations 205 (2004), no. 2, 271–297.
  • Caraballo, Tomás; Kloeden, Peter E.; Schmalfuß, Björn Exponentially stable stationary solutions for stochastic evolution equations and their perturbation. Appl. Math. Optim. 50 (2004), no. 3, 183–207.
  • Caraballo, Tomás; Robinson, James C. Stabilisation of linear PDEs by Stratonovich noise. Systems Control Lett. 53 (2004), no. 1, 41–50.
  • Caraballo, Tomás; Langa, José A.; Taniguchi, Takeshi The exponential behaviour and stabilizability of stochastic 2D-Navier-Stokes equations. J. Differential Equations 179 (2002), no. 2, 714–737.
  • Caraballo, Tomás; Langa, José A.; Robinson, James C. Attractors for differential equations with variable delays. J. Math. Anal. Appl. 260 (2001), no. 2, 421–438.
  • Caraballo, Tomás; Langa, José A.; Robinson, James C. A stochastic pitchfork bifurcation in a reaction-diffusion equation. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 457 (2001), no. 2013, 2041–2061.
  • Caraballo, Tomás; Langa, José A.; Robinson, James C. Upper semicontinuity of attractors for small random perturbations of dynamical systems. Comm. Partial Differential Equations 23 (1998), no. 9-10, 1557–1581. 

For a complete list of publications, visit: 
https://personal.us.es/caraball/tcgpublic.html 

Bibliometric data (January 2021):

  ISI Web of Knowledge: 
 Number of publications: 232                  Total number of citations: 3976                   h-index: 35 

   Scopus: 
 Number of publications: 227                  Total number of citations: 3981                  h-index: 35