FAU DCN-AvH workshop: Analysis, Numerics and Control

Date: Fri. June 30, 2023:

Event: FAU DCN-AvH Mini-workshop: Analysis, Numerics and Control
Organized by: FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

11:35H
Title: Stability of Elastic Systems with Local Damping
Speaker: Prof. Dr. Qiong Zhang
Affiliation: Visiting Scientist at FAU DCN-AvH from Beijing Institute of Technology.

Slides

Abstract. In this talk we consider the polynomial stability for several elastic systems with local damping. By establishing precise estimates on the resolvent, we prove polynomial decay of the corresponding semigroup. The results reveal that the rate of decay depends strongly on the coefficient function and location of damping.

12:00H
Title: On the wave turbulence theory for a stochastic KdV type equation
Speaker: Prof. Dr. Minh-Binh Tran
Affiliation: Visiting Scientist at FAU DCN-AvH from Texas A&M University (TAMU).

Abstract. Starting from the stochastic Zakharov-Kuznetsov equation, a multidimensional KdV type equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We show that the two point correlation function can be asymptotically expressed as the solution of the 3-wave kinetic equation at the kinetic limit under very general assumptions: the initial condition is out of equilibrium, the dimension is d≥2, the smallness of the nonlinearity λ is allowed to be independent of the size of the lattice, the weak noise is chosen not to compete with the weak nonlinearity and not to inject energy into the equation. To the best of our knowledge, the work provides the first rigorous derivation of nonlinear 3-wave kinetic equations. Also this is the first derivation for wave kinetic equations in the lattice setting and out-of-equilibrium. This is joint work with Gigliola Staffilani (MIT).

12:25H
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.

Slides

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 $L^1$ -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.

WHERE?

On-site / Online

[On-site] Room 01.151. FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg.
GPS-Koord. Raum: 49.573732N, 11.029867E
Cauerstraße 11, 91058 Erlangen.

[Online] Zoom meeting link
Meeting ID: 614 4658 1599 | PIN code: 914397

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