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Workshops

De Cadedif

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

Última versión de 07:37 19 oct 2008


  • Jornada de Dinámica Infinito Dimensional
Martes 27 de Noviembre de 2007, Departamento de Matemática Aplicada, UCM. 9:30-13:25, [cartel]


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