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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Entropy-Dissipation Informed Neural Networks for McKean-Vlasov type PDEs
McKean-Vlasov型 偏微分方程 熵耗散 信息神经网络
2023/4/13
We extend the concept of self-consistency for the Fokker-Planck equation (FPE) [Shen et al., 2022] to the more general McKean-Vlasov equation (MVE). While FPE describes the macroscopic behavior of par...
ABSENCE OF ANOMALOUS DISSIPATION OF ENERGY IN FORCED TWO DIMENSIONAL FLUID EQUATIONS
ABSENCE OF ANOMALOUS DISSIPATION OF ENERGY FORCED TWO DIMENSIONAL FLUID EQUATIONS
2014/4/3
Anomalous dissipation of energy in three dimensional turbulence is one of the basic statements of physical theory [55]. It has been veri ed experimentally to a large degree [75], but not mathematicall...
On the Production of Dissipation by Interaction of Forced Oscillating Waves in Fluid Dynamics
Equations of mixed hyperbolic and parabolic type oscillations BKW Calculus stability
2011/8/25
Abstract: In the context of some bidimensionnal Navier-Stokes model, we exhibit a family of exact oscillating solutions $\{u_{\epsilon}\}_{\epsilon}$ defined on some strip $[0,T]\times\R^2$ which does...
In-flight dissipation as a mechanism to suppress Fermi acceleration
In-flight dissipation mechanism suppress Fermi acceleration
2010/11/10
Some dynamical properties of time-dependent driven elliptical-shaped billiard are studied. It was shown that for the conservative time-dependent dynamics the model exhibits the Fermi acceleration [Ph...
Zero dissipation limit to rarefaction wave with vacuum for 1-D compressible Navier-Stokes equations
rarefaction wave vacuum for 1-D compressible Navier-Stokes equations
2010/11/15
It is well-known that one-dimensional isentropic gas dynamics has two elementary waves, i.e., shock wave and rarefaction wave. Among the two waves, only the rarefaction wave can be connected with vac...
On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurements
Lossless Approximations Fluctuation-Dissipation Theorem Limitations of Measurements
2010/12/6
In this paper, we take a control-theoretic approach to answering some standard questions in statistical mechanics, and use the results to derive limitations of classical measurements.
Influence of nonlinear dissipation and external perturbations onto transition scenarious to chaos in Lorenz-Haken system
nonlinear dissipation Lorenz-Haken system external perturbations
2010/4/2
We study an influence of nonlinear dissipation and external perturbations onto transition scenarious to chaos in Lorenz-Haken system. It will be show that varying in external potential parameters valu...
Energy Decay of Solutions of a Wave Equation of $p$-Laplacian Type with a Weakly Nonlinear Dissipation
Wave equation of $p$-Laplacian type Decay rate
2008/7/1
In this paper we study decay properties of the solutions to the wave equation of p-Laplacian type with a weak nonlinear dissipative.
Dissipation and Decay Estimates
Partial differential equations global solutions decay estimates Fourier splitting technique
2007/12/11
We establish the optimal rates of decay estimates ofglobal solutions of some abstract differential equations, whichinclude many partial differential equations. We provide a generaltreatment so that an...