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GEDA (Grupo de ecuaciones diferenciales y aplicaciones) is a research team made up of people of three different universities headquartered in the Mathematics department of the Carlos III University.

The research will focus on a series of lines originated from the mathematical models of nonlinear diffusion, especially of degenerate, singular type or with geometrical origin, as well as nonlocal diffusion and the associated stationary states. Our main interests are qualitative theory (existence, uniqueness, multiplicity, regularity), the study of free boundaries, the formation of singularities in finite time and the asymptotic behaviour. Existence of positive bound and ground state solutions of systems with linearly and nonlinearly coupled nonlinear Schrödinger (NLS) and  NLS-KdV equations. Also we are interested in stability properties of some dispersive systems.

Research Lines

  • Non-linear elliptic and parabolic equations
    Semilinear PDE's involving Caffarelli-Khon-Nirenberg (CKN) weights (E. Colorado)
    Quasilinear PDE's including the p-Laplacian operator (E. Colorado, A. de Pablo)
    Porous medium equations (A. de Pablo)
    Problems with mixed Dirichlet-Neumann type boundary conditions (E. Colorado)
    Spatial heterogeneities for cooperative systems (P. Álvarez-Caudevilla)
    Existence, multiplicity and regularity of solutions (P. Álvarez-Caudevilla, C. Brändle, E. Colorado, A. de Pablo)
    Bifurcation theory (P. Álvarez-Caudevilla, E. Colorado)
    Blow-up in reaction-diffusion equations (A. de Pablo)
    Stability properties of blow-up (A. de Pablo)
    Higher order PDE's (thin film, Cahn-Hilliard, Schrödinger) (P. Álvarez-Caudevilla, E. Colorado)
  • Fractional and non-local operators
    Nonlinear problems related to the fractional Laplacian (C. Brändle, E. Colorado, A. de Pablo)
    Fractional porous medium equation (A. de Pablo)
    Existence, multiplicity and regularity of solutions (C. Brändle, E. Colorado, A. de Pablo)
  • Dispersive systems
    Systems of coupled NLS and NLS-KdV equations (E. Colorado)
    Soliton solutions, bound and ground states (E. Colorado)
    Existence, multiplicity of solutions (E. Colorado)
  • Stochastic equations and Lévy processes (C. Brändle)

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