arXiv subjects

Cuncai Liu

Publications and source records attributed to Cuncai Liu.

3 recordsLinked to original sources

arXiv2025

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

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

math.AP↗

arXiv2025

Long-term behavior for wave equation with nonlinear damping and super-cubic nonlinearity

In this paper, we consider the semilinear wave equation involving the nonlinear damping term $g(u_t) $ and nonlinearity $f(u)$. The well-posedness of the weak solution satisfying some additional regularity is achieved under the wider ranges of the exponents $g$ and $f$. Moreover, the existence of global attractor and exponential attractor are proved.

math.AP↗

arXiv2023

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

This study investigates a semilinear wave equation characterized by nonlinear damping $g(u_t) $ and nonlinearity $f(u)$. First, the well-posedness of weak solutions across broader exponent ranges for $g$ and $f$ is established, by utilizing a priori space-time estimates. Moreover, the existence of a global attractor in the phase space $H^1_0(\Omega)\times L^2(\Omega)$ is obtained. Furthermore, it is proved that this global attractor is regular, implying that it is a bounded subset of $(H^2(\Omega)\cap H^1_0(\Omega))\times H^1_0(\Omega)$.

math.AP↗