GAFEVOL 2022: Dissipation, Decay and Hypocoercivity for Hyperbolic Systems by E. Zuazua
On Wednesday November 30, 2022 our Head Prof. Enrique Zuazua will talk on “Dissipation, Decay and Hypocoercivity for Hyperbolic Systems” as invited speaker at the XV Congress GAFEVOL 2022, Evolution Equations and Functional Analysis Group from November 28th to December 2nd, 2022 organized -in hybrid mode- by Universidad Nacional de Colombia Sede Manizales, Universidad del Norte and Universidad de Santiago de Chile at Manizales, Colombia.
Abstract. We will discuss the time-asymptotic behavior of linear hyperbolic systems under localized partial dissipation. We will show how the problem can be handled using Fourier analysis and propagation along characteristics. A sharp understanding of the decay rates requires the employment of concepts in control theory, such as the classical rank condition for controllability. Avoiding the use of the Fourier transform in the proofs, something that is relevant when aiming for more general results, in particular for nonlinear systems, requires the use of hypocoercivity tools.
 K. Beauchard y E. Zuazua, Sharp large time asymptotics for partially dissipative hyperbolic systems, Arch. Rational Mech. Anal., 199 (2011) 177–227.
 A. Porretta y E. Zuazua, Numerical hypocoercivity for the Kolmogorov equation, Mathematics of Computation, AMS, Volume 86, Number 303, January 2017, 97–119, http://dx.doi.org/10.1090/mcom/3157.
 Th. Crin-Barac, N. de Nitti, E. Zuazua, On the decay of one-dimensional locally and partially dissipative hyperbolic systems, https://arxiv.org/abs/2206.00555.
Check all details at the official page of the event