• Seminarios del 2016-2017

  • Autor: Juan Belmonte Beitia, UCLM
    Título: Dynamics and Optimal Control of chemotherapy for low grade gliomas
    Fecha:20 de Septiembre a las 12:00
    Lugar: Aula 209
    We discuss the optimization of chemotherapy treatment for low- grade gliomas using a mathematical model. We analyze the dynamics of the model and study the stability of solutions. The dynamical model is incor- porated into an optimal control problem for which different objective func- tionals are considered. We establish the existence of optimal controls and give a detailed discussion of the necessary optimality conditions. Since the control variable appears linearly in the control problem, optimal controls are concatenations of bang-bang and singular arcs. We derive a formula of the singular control in terms of state and adjoint variables. Using discretization and optimization methods we compute optimal drug protocols in a number of scenarios. For small treatment periods, the optimal control is bang-bang, whereas for larger treatment periods we obtain both bang-bang and singular arcs. In particular, singular controls illustrate the metronomic chemotherapy.

  • Autor: Workshop:Nonlinear Partial Differential Equations
    Título: organizado por Julian López-Gómez (UCM)
    Fecha:23 de Septiembre a las 10:00-13:30
    Lugar: Aula 209
      1. 10:00 S. Fernández-Rincón (UCM, Madrid) A singular perturbation result in competition theory.
      2. 10:40 L. Maire (UCM, Madrid) Coupled versus uncoupled blow-up rates in cooperative logistic systems with n species.
      3. 11:20 A. Tellini (CNRS-EHESS, Paris) High multiplicity and bifurcation diagrams for positive solutions to a class of superlinear indefinite problems.
      4. 12:00-12:30 Coffe break.
      5. 12:30 E. N. Dancer (US, Sydney) The exact number of stable positive solutions for nonlinear elliptic partial differential equations with small diffusion.
      6. (Opening Ceremony of the Seminar of Applied Mathematics, 2016-17)

  • Autor: Marcos A. Capistrán, CIMAT
    Título: Un problema inverso que surge en la reflexión y transmisión de ondas por un medio estratificado
    Fecha:4 Octubre a las 12:30
    Lugar: Aula 209
    Exploramos la exactitud de las fórmulas explícitas, introducidas por Pham et al (2015), para la amplitud de ondas transmitidas y reflejadas a través de una pila de capas homogéneas e isotrópicas para aproximar la respuesta de materiales estratificados (FGM). En consecuencia, hacemos muestreo de un modelo Bayesiano de un coeficiente de Lame del FGM bajo el supuesto de que los coeficientes de Lame tienen forma polinómica.

  • Autor: Ernesto Nungesser, ICMAT
    Título: Late-time behaviour for homogeneous solutions of the Einstein-Boltzmann system with and without cosmological constant
    Fecha:25 Octubre a las 12:00
    Lugar: Aula 209
    We will present the Einstein-Boltzmann system with and without cosmological constant and discuss recent results on this system in collaboration with Ho Lee. [cf.Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry and Late-time behaviour of Israel particles in a FLRW spacetime with Λ>0]

  • Autor:Juan Luis Vázquez (UAM)
    Titulo:Linear and nonlinear diffusion with fractional and nonlocal operators
    Lugar:Sala 209
    Fecha: 17-01-2017 a las 11:00
    We report on some of the progress made by the author and collaborators on the topic of nonlinear diffusion equations involving long distance interactions in the form of fractional Laplacian operators. The heat equation is the well-established paradigm for heat transportation and diffusion processes. The probabilistic model behind it is the Brownian motion. Diffusion equations involving non-local effects, hence non-Brownian processes, have been studied for a number of years but only recently they have become the object of intense work in mathematical analysis. Results cover well-posedness, regularity, free boundaries, asymptotics, extinction, and others. Differences with standard diffusion have been specially examined. We will end the presentation with the problems on bounded domains which offer interesting challenges that we are exploring.

  • Seminario de Departamento
    Autor:Pier Domenico Lamberti.
    Titulo: On the Lp Hardy inequality.
    Lugar:Sala 209
    Fecha: 14-03-2017
    Hora: 11:00.

    In this talk we present a few stability results, jointly obtained with Gerassimos Barbatis, concerning the dependence of Hp(Ω ) upon variation of p and Ω, with special attention to non-convex domains (in which case the value of Hp(Ω ) is in general not explicitly known).

    Time permitting, we shall also present some results obtained with Yehuda Pinchover devoted to the generalization of a few classical results to the case of C1,α domains.

  • Coloquio ICMAT-UCM
    Autor:Alfonso Castro (Claremont, EE. UU. y Cátedra de Excelencia de la Comunidad de Madrid-UCM)
    Titulo:Existencia de siete soluciones para un problema de dirichlet semilineal
    Lugar:Aula Miguel de Guzmán
    Fecha: 16-03-2017
    Hora: 12:00.
    Utilizando diversas herramientas de la teoría de puntos críticos, demostramos la existencia de siete soluciones para una clase de problemas elípticos asintóticamente lineales. El lema del paso de montaña, el método de reducción y la variedad de Nehari son ampliamente utilizados.

  • Seminario de Matemática Aplicada
    Autor:José Ignacio Tello (Universidad Politécnica de Madrid)
    Titulo:Inverse problems in reynolds equations: new results and perspectives
    Lugar:Sala 209 (Seminario Alberto Dou)
    Fecha: 21-03-2017
    Hora: 11:00.
    Reynolds equation describes the behavior of a the pressure of a fluid filling the gap between two surface in relative motion and close proximity. If the distance between both surfaces is known, the problem presents uniqueness of solutions under suitable assumptions in the geometry. If we allow to the surface to move with one, two or three degrees of freedom the coefficients of the equation depend indirectly of the solution, in that case Reynolds equation is copied to a Newtons second Law. We present results on existence of solutions for a range of parameters and some open problems.
    Organizado por el IMI y el Departamento de Matemática Aplicada, con la colaboración del grupo UCM MOMAT