Heat and wave processes: Some connections
speaker: Enrique Zuazua (Basque Center for Applied Mathematics)abstract: One of the main distinguishing aspects of some applications in engineering and other sciences is that evolving phenomena have to be understood in a long time horizon. In this lecture we shall present recent joint work with L. Ignat and A. Pozo showing that, for hyperbolic conservation laws, some numerical schemes that are well known to converge in finite time intervals, fail to capture the correct large time dynamics. This is due to the fact that numerical schemes, as time evolves, add artificial viscosity that, ultimately, makes the discrete dynamics to be of parabolic nature, rather than hyperbolic.
Connections between parabolic and hyperbolic equation equations are also relevant in other contexts such as Control or Inverse Problems theories. We shall also present an inverse Kannai transform allowing to write the solutions of the wave equation in terms of those of the heat equation. This has some interesting consequences for the problem of observing solution from boundary measurements. This is a joint work with S. Ervedoza.
timetable:
Thu 4 Jul, 9:00 - 9:50, Aula Dini
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