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| - | ==iMdea matemáticas:seminario 29 de noviembre 2007 ==
| + | __NOTOC__ |
| | | | |
| | + | *<big><u>Jornada de Dinámica Infinito Dimensional</u></big> |
| | + | ::Martes 27 de Noviembre de 2007, Departamento de Matemática Aplicada, UCM. 9:30-13:25, [[Media:jornada_27nov2007_2-3.pdf | [cartel]]] |
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| - | <center>
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| - | Dpto. de Matemáticas, sala 520 Facultad de Ciencias - UAM Ciudad
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| - | Universitaria de Cantoblanco 28049 Madrid
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| - | </center>
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| | + | <!-- |
| | + | == Jornada de Dinámica Infinito Dimensional: Martes 27 de Noviembre de 2007== |
| | | | |
| - | '''10:30 · 11:10 Hardy inequalities in twisted waveguides'''
| |
| | <center> | | <center> |
| | + | Departamento de Matemática Aplicada Universidad Complutense de Madrid |
| | | | |
| - | David KREJ CIRÍK
| + | Jornada de Dinámica Infinito Dimensional |
| - | Department of Theoretical Physics, Nuclear Physics Institute, Academy
| + | Martes 27 de Noviembre de 2007 |
| - | of Sciences, Rez, Czech Republic e-mail: krejcirik@ujf.cas.cz
| + | |
| | + | Lugar: Sala 209, |
| | + | |
| | + | Seminario del Departamento de Matemática Aplicada |
| | + | |
| | + | Facultad de Ciencias Matemáticas, UCM |
| | </center> | | </center> |
| | | | |
| | + | '''9:30-10:20. "Attractors for Parabolic Problems in dumbbell domains", ''' |
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| - | The Dirichlet Laplacian in tubular domains is a simple but remarkably
| + | German Lozada, Univ. Del Estado de Sao Paulo, Brasil |
| - | successful model for the quantum Hamiltonian in mesoscopic waveguide
| + | |
| - | systems. We make an overview of geometrically induced Hardy-type
| + | |
| - | inequalities established recently for the Laplacian in twisted tubes,
| + | |
| - | and mention consequences for the electronic transport. We begin by
| + | |
| - | recalling the classical Hardy inequality and its relation to
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| - | geometric, spectral, stochastic and other properties of the underlying
| + | |
| - | Euclidean space. After discussing the complexity of the problem when
| + | |
| - | reformulated for quasi-cylindrical subdomains, we give a proof of the
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| - | Hardy inequality due to a twist of three-dimensional tubes of uniform
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| - | cross-section and use it to prove certain stability of the spectrum.
| + | |
| - | We also discuss similar effects induced by curvature of the ambient
| + | |
| - | space or switch of boundary conditions.
| + | |
| | | | |
| - | '''11:10 · 11:50 Existence and continuity of global attractors for a class of non local evolution equations ''' | + | '''10:20-11:10. "Semilinear Damped Wave Equations with nonlinearities", ''' |
| | | | |
| - | <center>
| + | Jan Cholewa, U. Silesia (Katowice), Polonia |
| - | Antônio L. PEREIRA
| + | |
| - | Instituto de Matemática e Estatística-USP
| + | |
| - | Rua do Matão, 1010, Cidade Universitária, São Paulo-SP,
| + | |
| - | Brasil e-mail: alpereir@ime.usp.br
| + | |
| - | </center>
| + | |
| - | In this work we prove the existence of a compact global attractor for
| + | |
| - | the flow of the equation
| + | |
| - | <center>
| + | |
| - | <math>
| + | |
| - | \frac{\partial m(r,t)}{\partial t} = -m(r,t)+g(\beta J*M(r,t)+\beta h)
| + | |
| - | \qquad h, \beta \geq 0
| + | |
| - | </math>
| + | |
| - | </center>
| + | |
| | | | |
| - | in
| + | '''11:15-11:45. Café ''' |
| - | <math>
| + | |
| - | L^{2}(S^{1}).
| + | |
| - | </math>
| + | |
| - | We also show that the flow is gradient and the global attractor
| + | |
| - | depends continuosly on the parameters h and . AMS subject
| + | |
| - | classification: 34G20,47H15.
| + | |
| | | | |
| - | '''11:50 · 12:10 Coffee break ''' | + | '''11:45-12:35. "Dynamical approach to elliptic BVP in asymptotically symmetric unbounded domains", ''' |
| | | | |
| | + | Messoud Efendiev, Technische Universistät München, Alemania |
| | | | |
| - | '''12:10 · 13:10 Creating materials with desired refraction coefficient''' | + | '''12:35-13:25. "Non simultaneous quenching in a system of heat equations coupled at the boundary", ''' |
| - | <center>
| + | |
| - | A. G. RAMM
| + | Raul Ferreira, U. Complutense |
| - | Mathematics Department, Kansas State University,
| + | |
| - | Manhattan, KS 66506-2602, USA
| + | Organiza: Grupo de Investigación CADEDIF de la UCM. Parcialmente |
| - | ramm@math.ksu.edu
| + | financiado por: Proyecto MTM 2006-08262, "Programa de financiación de |
| - | </center> | + | Grupos de Investigación UCM-Comunidad de Madrid GR69/06-920894" y |
| | + | Departamento de Matemática Aplicada, UCM Más información: José M. |
| | + | Arrieta arrieta@mat.ucm.es Anibal Rodriguez Bernal arober@mat.ucm.es |
| | + | |
| | + | |
| | + | |
| | + | |
| | + | <center> '''ABSTRACTS ''' </center> |
| | + | '''"Attractors for Parabolic Problems in dumbbell domains" ''' |
| | + | |
| | + | German Lozada, Univ. del Estado de Sao Paulo, Brasil |
| | + | |
| | + | In this talk we analyze the dynamics of a parabolic equation with |
| | + | homogeneous Neumann boundary conditions in the dumbbell domain. We |
| | + | provide an appropriate functional setting to treat this problem and |
| | + | show that the attractors behave upper semicontinuous as the channel |
| | + | shrinks to a line segment. |
| | + | |
| | + | '''"Semilinear Damped Wave Equations with fast growing Cholewa, U. |
| | + | Silesia (Katowice), Polonia nonlinearities" ''' |
| | + | |
| | + | Jan Cholewa, U. Silesia (Katowice), Polonia |
| | + | |
| | + | A class of the second order in time semilinear partial differential |
| | + | equations is considered in the Banach space setting. The results |
| | + | concerning local existence, regularity, bootstrapping continuation, |
| | + | and asymptotic properties of solutions are discussed in case when the |
| | + | nonlinear term satisfies certain critical growth conditions. |
| | + | |
| | + | '''"Dynamical approach to elliptic BVP in asymptotically symmetric unbounded domains", ''' |
| | + | |
| | + | Messoud Efendiev, Technische Universistät München, Alemania |
| | + | |
| | + | We consider dynamical approach to the elliptic problem in |
| | + | asymptotically symmetric unbounded domain and study the large-time |
| | + | behaviour of solutions. Due to the lack of the uniqueness of the |
| | + | solutions the standard approach based both on the semigroup theory and |
| | + | on elliptic machinery fails. Our approach based on the trajectory |
| | + | dynamical systems. Symmetrization and stabilization of the solitions |
| | + | as well as open problem will also be discussed. |
| | + | |
| | + | '''"Non simultaneous quenching in a system of heat equations coupled at the boundary", ''' |
| | | | |
| - | A method is given for calculation of a distribution of small impedance
| + | Raul Ferreira, U. Complutense |
| - | particles, which should be embedded in a bounded domain, filled with
| + | |
| - | material with known refraction coefficient, in order that the
| + | |
| - | resulting new material would have a desired refraction coefficient.
| + | |
| - | The new material may be created so that it has some desired
| + | |
| - | wave-focusing properies. For example, it can scatter plane wave mostly
| + | |
| - | in a fixed solid angle. The inverse scattering problem with scattering
| + | |
| - | data given at a fixed wave number and at a fixed incident direction is
| + | |
| - | formulated and solved.
| + | |
| | | | |
| - | [http://www.imdea.org iMdea]
| + | We study the formation of singularities in finite time for solutions |
| | + | of the heat equations coupled at the boundary through a nonlinear flux |
| | + | at one border and zero flux at the other border. We characterize, in |
| | + | terms of the parameters involved when non-simultaneous quenching may |
| | + | appear. Moreover, if quenching is non-simultaneous we find the |
| | + | quenching rate and the quenching set. We also find a possible |
| | + | continuation after quenching of the solutions. Joint work with A. de |
| | + | Pablo, Mayte Pérez-Llanos, F. Quirós and J. D. Rossi. |
| | + | --> |
