Partial Differential Equations Seminar
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Mon, 10/10/2011 17:00 |
William W. Symes (Rice University) |
Partial Differential Equations Seminar  |
Gibson 1st Floor SR |
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Mon, 17/10/2011 17:00 |
Helge Holden (Norwegian University of Science and Technology) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
We prove existence of a global semigroup of conservative solutions of the nonlinear variational wave equation  . The equation was derived by Saxton as a model for liquid crystals. This equation shares many of the peculiarities of the Hunter–Saxton and the Camassa–Holm equations. In particular, the equation possesses two distinct classes of solutions denoted conservative and dissipative. In order to solve the Cauchy problem uniquely it is necessary to augment the equation properly. In this talk we describe how this is done for conservative solutions. The talk is based on joint work with X. Raynaud. |
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Mon, 24/10/2011 17:00 |
Hung Tran (University of California, Berkeley) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
| This is a joint work with Craig Evans. We study the partial regularity of minimizers for certain functionals in the calculus of variations, namely the modified Landau-de Gennes energy functional in nematic liquid crystal theory introduced by Ball and Majumdar. | |||
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Mon, 31/10/2011 17:00 |
Yaroslav Kurylev (University College, London) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
| We consider the mathematical theory of invisibility. We start with singular transformation which provide exact (both active and passive) invisibility. We then show how to approximate this highly anisotropic, singular material parameters with homogeneous non-singular ones. We then apply this construction to produce some unusual phenomena in quantum physics, acoustics, etc. (like invisible sensor and Schrodinger Hat potential) | |||
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Mon, 07/11/2011 17:00 |
Tim Palmer (University of Oxford and European Centre for Medium-Range Weather Forecasts) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
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Mon, 14/11/2011 17:00 |
Vicentiu D. Radulescu (Simion Stoilow Mathematics Institute of the Romanian Academy) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
| We describe several bifurcation properties corresponding to various classes of nonlinear elliptic equations The purpose of this talk is two-fold. First, it points out different competition effects between the terms involved in the equations. Second, it provides several non standard phenomena that occur according to the structure of the differential operator. | |||
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Mon, 28/11/2011 17:00 |
Kirill Cherednichenko (Cardiff University) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
I will describe a multiscale asymptotic framework for the analysis of the macroscopic behaviour of periodic
two-material composites with high contrast in a finite-strain setting. I will start by introducing the nonlinear
description of a composite consisting of a stiff material matrix and soft, periodically distributed inclusions. I shall then focus
on the loading regimes when the applied load is small or of order one in terms of the period of the composite structure.
I will show that this corresponds to the situation when the displacements on the stiff component are situated in the vicinity
of a rigid-body motion. This allows to replace, in the homogenisation limit, the nonlinear material law of the stiff component
by its linearised version. As a main result, I derive (rigorously in the spirit of  -convergence) a limit functional
that allows to establish a precise two-scale expansion for minimising sequences. This is joint work with M. Cherdantsev and
S. Neukamm. |
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