Les Equacions en Derivades Parcials, EDPs, són una de las eines fonamentals de la modelització matemàtica en Biologia, Física, Química, Economia i Indústria. El seu estudi analític i les seves aplicacions formen l'eix del grup de recerca. El nostre interés central són les EDPs no lineals amb difusió standard o fraccionària i les EDPs de primer ordre amb termes no-locals. Estudiem el seu orígen i aplicacions en problemes de reacció, en biologia matemàtica, dinàmica de poblacions, problemes geomètrics, dinàmica d'ones, i models de formació de preus.

http://futur.upc.edu/EDP

Enviaments recents

  • Quintessential inflation at low reheating temperatures 

    Aresté Saló, Llibert; Haro Cases, Jaume (2017-11-23)
    Article
    Accés obert
    We have tested some simple quintessential inflation models, imposing the requirement that they match with the recent observational data provided by the BICEP and Planck team and leading to a reheating temperature, which ...
  • Reheating via gravitational particle production in simple models of quintessence or ¿CDM Inflation 

    Haro Cases, Jaume; Aresté Saló, Llibert (2017-11-14)
    Article
    Accés obert
    We have tested some simple CDM (the same test is also valid for quintessence) inflation models, imposing that they match with the recent observational data provided by the BICEP and Planck’s team and leading to a reheating ...
  • Delaunay hypersurfaces with constant nonlocal mean curvature 

    Cabré Vilagut, Xavier; Fall, Mouhamed Moustapha; Weth, Tobias (2017-08-12)
    Article
    Accés restringit per política de l'editorial
    We study hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated with critical points of the fractional perimeter functional under a volume constraint. We establish the ...
  • The matter-ekpyrotic bounce scenario in Loop Quantum Cosmology 

    Haro Cases, Jaume; Amorós Torrent, Jaume; Aresté Saló, Llibert (2017-09-01)
    Article
    Accés restringit per política de l'editorial
    We will perform a detailed study of the matter-ekpyrotic bouncing scenario in Loop Quantum Cosmology using the methods of the dynamical systems theory. We will show that when the background is driven by a single scalar ...
  • Viscous cosmology for early- and late-time universe 

    Brevik, Iver; Grøn, Øyvind; Haro Cases, Jaume; Odintsov, Sergei D.; Saridakis, Emmanuel N. (2017-01-01)
    Article
    Accés restringit per política de l'editorial
    point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (exluding special cases such as superconductivity). ...
  • Pohozaev identities for anisotropic integrodifferential operators 

    Ros Oton, Xavier; Serra Montolí, Joaquim; Valdinoci, Enrico (2017-08-15)
    Article
    Accés restringit per política de l'editorial
    We find and prove new Pohozaev identities and integration by parts type formulas for anisotropic integrodifferential operators of order 2s, with s¿(0,1). These identities involve local boundary terms, in which the quantity ...
  • L-p estimates for the variation for singular integrals on uniformly rectifiable sets 

    Mas Blesa, Albert; Tolsa, Xavier (2017-11-01)
    Article
    Accés obert
    The L^p(1<p<\infty) and weak- L^1 estimates for the variation for Calderón-Zygmund operators with smooth odd kernel on uniformly rectifiable measures are proven. The L^2 boundedness and the corona decomposition method are ...
  • Boundedness of stable solutions to semilinear elliptic equations: A survey 

    Cabré Vilagut, Xavier (2017-05-01)
    Article
    Accés obert
    This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known L8 estimates that hold for all nonlinearities. Such estimates are ...
  • Boundary regularity estimates for nonlocal elliptic equations in C1 and C1, domains 

    Ros-Oton, Xavier; Serra Montolí, Joaquim (2017-02-04)
    Article
    Accés restringit per política de l'editorial
    We establish sharp boundary regularity estimates in C1 and C1,a domains for nonlocal problems of the form Lu=f in O, u=0 in Oc. Here, L is a nonlocal elliptic operator of order 2s, with s¿(0,1). First, in C1,a domains we ...
  • Dirac operators, shell interactions, and discontinuous gauge functions across the boundary 

    Mas Blesa, Albert (2017-02-01)
    Article
    Accés obert
    Given a bounded smooth domain Ω ⊂ R3, we explore the relation between couplings of the free Dirac operator −iα · ∇ + mβ with pure electrostatic shell potentials λδ∂Ω (λ ∈ R) and some perturbations of those potentials given ...
  • Differentiability with respect to parameters in global smooth linearization 

    Rodrigues, Hildebrando M.; Solà-Morales Rubió, Joan de (2017-03-15)
    Article
    Accés restringit per política de l'editorial
    Let XX be a Banach space and T¿:X¿XT¿:X¿X a family of invertible contractions, T¿=L¿+f¿T¿=L¿+f¿, where L¿L¿ is linear and f¿f¿ is nonlinear with f¿(0)=0f¿(0)=0. We give conditions for the existence of a family of global ...
  • Teleparallel loop quantum cosmology in a system of intersecting branes 

    Haro Cases, Jaume (Elsevier, 2016-09-10)
    Article
    Accés restringit per política de l'editorial
    Recently, some authors have removed the big bang singularity in teleparallel Loop Quantum Cosmology (LQC) and have shown that the universe may undergo a number of oscillations. We investigate the origin of this type of ...

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