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Stabilization of the critical and subcritical semilinear inhomogeneous and anisotropic elastic wave equation
Zhen-Hu Ning, Fengyan Yang, Jiacheng Wang
{\bf Abstract} \,\,We prove exponential decay of the critical and subcritical semilinear inhomogeneous and anisotropic elastic wave equation with locally distributed damping on bou…
Special uniform decay rate of local energy for the wave equation with variable coefficients on an exterior domain
Zhen-Hu Ning, Fengyan Yang, Xiaopeng Zhao
We consider the wave equation with variable coefficients on an exterior domain in (). We are interested in finding a special uniform decay rate of local energy differ…
Asymptotic behavior of the nonlinear Schrödinger equation on exterior domain
Zhen-Hu Ning
{\bf Abstract} \,\, We consider the following nonlinear Schrödinger equation on exterior domain. \begin{equation} \begin{cases} iu_t+Δ_g u + ia(x)u - |u|^{p-1}u = 0 \qquad (x,t) \i…
Escape Metrics and its Applications
Zhen-Hu Ning, Fengyan Yang, Xiaopeng Zhao
Geodesics escape is widely used to study the scattering of hyperbolic equations. However, there are few progresses except in a simply connected complete Riemannian manifold with no…