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Exponential mixing for random nonlinear wave equations: weak dissipation and localized control

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arxiv 2407.15058 v1 pith:UOO4SNOU submitted 2024-07-21 math.AP math.DSmath.OCmath.PR

Exponential mixing for random nonlinear wave equations: weak dissipation and localized control

Ziyu Liu , Dongyi Wei , Shengquan Xiang , Zhifei Zhang , Jia-Cheng Zhao This is my paper
classification math.AP math.DSmath.OCmath.PR
keywords equationsexponentiallocalizedmixingrandomsystemscontrolcriterion
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We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics, i.e., asymptotic compactness in dynamical systems, global stability of evolution equations, and localized control problems. As an initial application, we exploit the exponential mixing of random nonlinear wave equations with degenerate damping, critical nonlinearity, and physically localized noise. The essential challenge lies in the fact that the weak dissipation and randomness interact in the evolution.

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Cited by 6 Pith papers

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