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:

  1. Dissipative mechanisms by balancing interior reaction, diffusion and nonlinear boundary conditions.
  2. Existence and stability of extremal equilibria for reaction diffusion equations in both bounded and unbounded domains.
  3. Dissipative mechanisms for second order parabolic problems in unbounded domains by balancing reaction and diffusion.
  4. 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.
  5. Dissipative mechanism in fourth order problems by energy balance between reaction and the bilaplacian.
  6. Singular perturbations in elliptic and parabolic problems.
  7. 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.
  8. Perturbation methods in evolution PDEs. Linear and nonlinear perturbed semigroups.

EVENTS

1234
567891011
12131415161718
19202122232425
262728293031


Subscribe to our Activities mailing list. Subscribe - Unsubscribe

Pequeño Instituto de Matemáticas

PIM

ICMAT in the elpais.es