Uniform attractors of non-autonomous Kirchhoff wave models

Zhijian Yang; Yanan Li; Na Feng

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arXiv · 1908.06500

Uniform attractors of non-autonomous Kirchhoff wave models

Zhijian Yang·Yanan Li·Na Feng

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Abstract

The paper investigates the existence and upper semicontinuity of uniform attractors of the perturbed non-autonomous Kirchhoff wave equations with strong damping and supercritical nonlinearity: $u_{tt}-\Delta u_{t}-(1+\epsilon\|\nabla u\|^{2})\Delta u+f(u)=g(x,t)$, where $\epsilon\in [0,1]$ is a perturbed parameter. It shows that when the nonlinearity $f(u)$ is of supercritical growth $p: \frac{N+2}{N-2}=p^*<p<p^{**}=\frac{N+4}{(N-4)^+}$: (i) the related evolution process has a compact uniform attractor $\mathcal{A}_\ls^\e $ for each $\epsilon\in [0,1]$; (ii) the family of uniform attractor $\mathcal{A}_\ls^\e $ is upper semicontinuous on the perturbed parameter $\epsilon$ in the sense of partially strong topology.

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Zhijian Yang, Yanan Li, Na Feng. 2019-08-18. Uniform attractors of non-autonomous Kirchhoff wave models. https://arxiv.org/abs/1908.06500

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