https://dcn.nat.fau.eu/events/mini-workshop-analysis-numerics-and-control-29-jun-2023/https://dcn.nat.fau.eu/events/mini-workshop-analysis-numerics-and-control-30-jun-2023/
15:20H
Title: Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis
Speaker: Prof. Dr. Ling-Yun Shou
Affiliation: Visiting Scientist at FAU DCN-AvH from Nanjing University of Aeronautics and Astronautics.
Abstract. We develop some new methods to establish time-decay estimates for partially dissipative hyperbolic systems on the real line. First, using the hyperbolic hypocoercivity approach, we recover natural time-decay estimates of solutions under the Kalman rank condition, without employing Fourier analysis and without assuming L1L^1L1-type conditions on the initial data. Furthermore, by means of space-weighted estimates and wave formulation, we establish enhanced time-decay rates subject to the initial data satisfying algebraic weighted conditions. As an application, this method enables us to obtain logarithmic time-decay rates of solutions for the nonlinearly damped p-system.
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