Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
|April 2018||June 2018|
Events for 11 May 2018
The talk is devoted to homogenization of solutions of periodic hyperbolic systems with rapidly oscillating coefficients. Classical results in homogenization theory looks as the convergence of solutions of the problem with rapidly oscillating coefficients to the solution of the so-called effective problem with constant coefficients. The constants in the corresponding error estimates depend on the differential operator, the lattice of periodicity, and the initial data somehow.
We are interested in the operator error estimates. In such estimates, dependence on the initial data in the error estimates is explicit: we have the norm of the data in error estimate. So, these estimates can be rewritten in operator terms.
The principal term of approximation for the solution of periodic hyperbolic systems was obtained by M. Birman and T. Suslina (2008). Our main result is approximation of solution in the energy norm. The corrector is taken into account. To obtain this approximation we have to assume that the initial data for the solution is equal to zero. The result can be written as approximation of the operator sine in the uniform operator topology with the precise order error estimate.
We use the spectral approach to homogenization problems developed by M. Sh. Birman and T. A. Suslina. The method is based on the scaling transformation, the Floquet-Bloch theory, and the analytic perturbation theory. It turns out that homogenization is a spectral threshold effect at the bottom of the spectrum.
More details: arXiv:1705.02531.
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