Longtime Dynamics of the Kirchhoff-Boussinesq-type Equation with Gentle Dissipation

DOI: https://doi.org/10.62517/jes.202602317

Author(s)

Na Feng*, Chendong Duan, Qi Feng

Affiliation(s)

School of Mathematics and Information Science, Zhongyuan University of Technology, Zhengzhou, China *Corresponding Author

Abstract

The paper studies longtime dynamics of the Kirchhoff-Boussinesq-type equation with gentle dissipation, which is a class of nonlinear hyperbolic equations arising in nonlinear elasticity and dispersion wave propagation. The Kirchhoff-Boussinesq model combine the nonlocal Kirchhoff stress term with the Boussinesq dispersion, while gentle dissipation characterized by fractional damped operators adds subtle energy decay mechanisms. By giving full play to the dissipative effect of gentle damping, we shall establish the regularity of solutions of the K-B equation when the growth exponents of nonlinearities are up to the best critical index. Furthermore, we discuss the global attractor for Kirchhoff-Boussinesq equation of parabolic equation characters. Finally, we highlight open problems concerning upper semicontinuity, unbounded domain, non-autonomous dynamics for future research. This paper aims to understand the complex asymptotic behavior of Kirchhoff-Boussinesq equations with multi-physical effects.

Keywords

Kirchhoff-Boussinesq Equation; Gentle Dissipation; Energy Solution; Global Attractor

References

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