Institution: UCM
Position: Catedrático de Universidad
Office: 105
Phone: +34 912999 725
Email: arober@mat.ucm.es
About:
My research activity revolves around partial differential equations (PDEs) of elliptic, parabolic or hyperbolic type with special emphasis on the dynamics of solutions, a field that could be briefly described as infinite dimensional dynamical systems. A big amount of work was centered on understanding dissipative mechanisms in PDEs that allow to construct the global attractor and to study some of its properties and/or structures that it contains.
Large blocks of work, not necessarily disjoint, that more or less reflect a chronological order are the following:
- Dissipative mechanisms by balancing interior reaction, diffusion and nonlinear boundary conditions.
- Existence and stability of extremal equilibria for reaction diffusion equations in both bounded and unbounded domains.
- Dissipative mechanisms for second order parabolic problems in unbounded domains by balancing reaction and diffusion.
- Well posedness of nonlinear parabolic problems. Critical exponents. Ill poshness of supercritical problems. Problems in uniform spaces. Second and fourth order problems. Higher order problems.
- Dissipative mechanism in fourth order problems by energy balance between reaction and the bilaplacian.
- Singular perturbations in elliptic and parabolic problems.
- Dissipative mechanisms for nonautonomous problems. Pullback attractors and non autonomous extremal solutions. Persistence and asymptotic behavior of logistic problems and non autonomous Lotka-Volterra type systems.
- Perturbation methods in evolution PDEs. Linear and nonlinear perturbed semigroups.
