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Zhijun Tang

Publications and source records attributed to Zhijun Tang.

4 recordsLinked to original sources
arXiv2023

Finite-dimensionality of attractors for wave equations with degenerate nonlocal damping

In this paper we study the fractal dimension of global attractors for a class of wave equations with (single-point) degenerate nonlocal damping. Both the equation and its linearization degenerate into linear wave equations at the degenerate point and the usual approaches to bound the dimension of the entirety of attractors do not work directly. Instead, we develop a new process concerning the dimension near the degenerate point individually and show the finite dimensionality of the attractor.

math.AP↗
arXiv2022

Strong attractors for weakly damped quintic wave equation in bounded domains

In this paper, we study the longtime dynamics for the weakly damped wave equation with quintic non-linearity in a bounded smooth domain of $\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded domains, we establish the existence of a strong global attractor in the phase space $H^2(Ω)\cap H^1_0(Ω)\times H^1_0(Ω)$. Moreover, the finite fractal dimension of the attractor is also shown with the help of the quasi-stable estimation.

math.AP↗
arXiv2022

Long-time dynamics of the wave equation with nonlocal weak damping and sup-cubic nonlinearity in 3-D domains

In this paper, we study the long-time dynamics for the wave equation with nonlocal weak damping and sup-cubic nonlinearity in a bounded smooth domain of $\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded domains, we first prove the global well-posedness of the Shatah-Struwe solutions. Then we establish the existence of the global attractor for the Shatah-Struwe solution semigroup by the method of contractive function. Finally, we verify the existence of a polynomial attractor for this semigroup.

math.AP↗