Now showing items 1-18 of 18

    • A Liouville type result for fractional Schrödinger operators in 1D 

      Felipe Navarro, Juan Carlos (Universitat Politècnica de Catalunya, 2017-01)
      Master thesis
      Open Access
      The aim of this master's thesis is to obtain an alternative and original proof of a Liouville type result for fractional Schrödinger operators in 1D without using a local extension problem, in the spirit of the recent work ...
    • A negative result for hearing the shape of a triangle 

      Orriols Giménez, Gerard (Universitat Politècnica de Catalunya, 2019-05-24)
      Bachelor thesis
      Open Access
      Covenantee:   Princeton University
      The project will consist of a mathematical research finding its place between the branches of Partial Differential Equations and Geometry, in particular dealing with inverse spectral problems of the Laplace operator. This ...
    • Black-Scholes differential equation and its development 

      Duaso Bellido, Mireia (Universitat Politècnica de Catalunya, 2015-07)
      Bachelor thesis
      Restricted access - author's decision
      L'equació de Black-Scholes és una equació en derivades parcials (EDP) de tipus difusió. Aquest model introdueix que els increments de l'actiu subjacent segueixen un moviment Brownià. És un mètode eficient per calcular el ...
    • Boundary regularity for the fractional heat equation 

      Fernández-Real Girona, Xavier (Universitat Politècnica de Catalunya, 2014-09)
      Bachelor thesis
      Open Access
      In this dissertation we present an introduction to nonlocal operators, and in particular, we study the fractional heat equation, which involves the fractional Laplacian of order 2s. In the first chapters we make a review ...
    • Delaunay cylinders with constant non-local mean curvature 

      Alvinyà Rubió, Marc (Universitat Politècnica de Catalunya, 2017-05)
      Master thesis
      Open Access
      The aim of this master's thesis is to obtain an alternative proof, using variational techniques, of an existence result for periodic sets in $\mathbb{R}^2$ that minimize a non-local version of the classical perimeter ...
    • La ecuación del calor 

      Caffarelli, Luis (2014-01-31)
      Other
      Open Access
      La ecuación del calor fue propuesta por Fourier en 1807-en su memoria sobre la propagación del calor en los cuerpos sólidos. En ella proponía además el germen de lo que pasaria a ser la Teoría de las Series de Fourier. Tan ...
    • Elliptic and parabolic PDEs : regularity for nonlocal diffusion equations and two isoperimetric problems 

      Serra Montolí, Joaquim (Universitat Politècnica de Catalunya, 2014-06-17)
      Doctoral thesis
      Open Access
      The thesis is divided into two parts. The first part is mainly concerned with regularity issues for integro-differential (or nonlocal) elliptic and parabolic equations. In the same way that densities of particles with ...
    • Estimates and rigidity for stable solutions to some nonlinear elliptic problems 

      Miraglio, Pietro (Universitat Politècnica de Catalunya, 2020-01-28)
      Doctoral thesis
      Open Access
      My thesis deals with the study of elliptic PDE. It is divided into two parts, the first one concerning a nonlinear equation involving the p-Laplacian, and the second one focused on a nonlocal problem. In the first part, ...
    • Ground states in Mathematical Physics 

      Doce Llisó, Edurne (Universitat Politècnica de Catalunya, 2015-09)
      Bachelor thesis
      Open Access
      The main aim of this bachelor's thesis is to introduce the concept of a ground state and prove its existence for the nonlinear diffusion equation $$ -\Delta u + a u = b |u|^\alpha u \ \ \text{in} \ \mathbb{R}^N, $$ as well ...
    • Integro-differential equations : regularity theory and Pohozaev identities 

      Ros Oton, Xavier (Universitat Politècnica de Catalunya, 2014-06-19)
      Doctoral thesis
      Open Access
      The main topic of the thesis is the study of Elliptic PDEs. It is divided into three parts: (I) integro-differential equations, (II) stable solutions to reaction-diffusion problems, and (III) weighted isoperimetric and ...
    • Minimizers to reaction-diffusion PDEs, Sobolev inequalities, and monomial weights 

      Ros Oton, Xavier (Universitat Politècnica de Catalunya, 2011-07)
      Master thesis
      Restricted access - author's decision
      Reaction-diffusion equations play a central role in PDE theory and its applications to other sciences. They also play an important role in geometric problems: the problem of prescribing a curvature on a manifold and parabolic ...
    • PDEs with fractional diffusion 

      Alvinyà Rubió, Marc (Universitat Politècnica de Catalunya, 2015-07)
      Bachelor thesis
      Open Access
      In recent years, there has been a surge of activity focused on the use of so-called fractional diffusion operators to replace the standard Laplace operator, with the aim of further extending the theory by taking into account ...
    • Periodic solutions to PDEs with fractional diffusion 

      Felipe Navarro, Juan Carlos (Universitat Politècnica de Catalunya, 2016-01)
      Bachelor thesis
      Open Access
      The aim of this Bachelor's Thesis is the study of periodic solutions to nonlinear equations involving the fractional Laplace operator. Our starting point is the Benjamin-Ono equation in water waves, a completely integrable ...
    • Propagation in reaction-diffusion equations with fractional diffusion 

      Coulon, Anne-Charline (Universitat Politècnica de Catalunya, 2014-07-07)
      Doctoral thesis
      Open Access
      Covenantee:   Université Toulouse III - Paul Sabatier
      This thesis focuses on the long time behaviour of solutions to Fisher-KPP reaction-diffusion equations involving fractional diffusion. This type of equation arises, for example, in spatial propagation or spreading of ...
    • Stable and periodic solutions to nonlinear equations with fractional diffusion 

      Sanz Perela, Tomás (Universitat Politècnica de Catalunya, 2016-07)
      Master thesis
      Open Access
      The aim of this thesis is to study stable solutions to nonlinear elliptic equations involving the fractional Lapacian. More precisely, we study the extremal solution for the problem $(\Delta )^s u = \lambda f(u)$ in $\Omega$, ...
    • Stable solutions of nonlinear fractional elliptic problems 

      Sanz Perela, Tomás (Universitat Politècnica de Catalunya, 2019-06-18)
      Doctoral thesis
      Open Access
      This thesis is devoted to study integro-differential equations. This type of equations constitutes nowadays a very active field of research which has important applications in modeling real-life phenomena where nonlocal ...
    • Topics on periodic solutions to integro-differential equations 

      Nualart Batalla, Marc (Universitat Politècnica de Catalunya, 2020-07)
      Master thesis
      Open Access
      This Master's Degree Thesis investigates periodic solutions to nonlinear equations involving integro-dierential operators. We show the existence and we describe these solutions for generalized Benjamin-Ono type nonlinearities, ...
    • Uncertainty quantification for stochastic systems 

      Jornet Sanz, Marc (Universitat Politècnica de Catalunya, 2018-10)
      Master thesis
      Restricted access - author's decision
      Random differential equations arise to model smooth random phenomena. The error term, instead of being introduced by means of a white noise, arises from imposing randomness to the input coefficients and initial/boundary ...