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arXiv · 2505.07255

Well-posedness and global attractor for wave equation with displacement dependent damping and super-cubic nonlinearity

Cuncai Liu·Fengjuan Meng·Chang Zhang
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Abstract

This work investigates the semilinear wave equation featuring the displacement dependent term $σ(u)\partial_t u $ and nonlinearity $f(u)$. By developing refined space-time a priori estimates under extended ranges of the nonlinearity exponents with $σ(u)$ and $f(u)$, the well-posedness of the weak solution is established. Furthermore, the existence of a global attractor in the naturally phase space $H^1_0(Ω)\times L^2(Ω)$ is obtained. Moreover, the regularity of the global attractor is established, implying that it is a bounded subset of $(H^2(Ω)\cap H^1_0(Ω))\times H^1_0(Ω)$.

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Cuncai Liu, Fengjuan Meng, Chang Zhang. 2025-05-12. Well-posedness and global attractor for wave equation with displacement dependent damping and super-cubic nonlinearity. https://arxiv.org/abs/2505.07255

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