Asymptotic behaviors of solutions to a sixth-order Boussinesq equation with logarithmic nonlinearity

Huan Zhang; Jun Zhou

doi:10.3934/cpaa.2021034

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2021, Volume 20, Issue 4: 1601-1631. Doi: 10.3934/cpaa.2021034

This issue Previous Article On weak solutions to a fractional Hardy–Hénon equation: Part I: Nonexistence Next Article Existence of multi-peak solutions to the Schnakenberg model with heterogeneity on metric graphs

Asymptotic behaviors of solutions to a sixth-order Boussinesq equation with logarithmic nonlinearity

Huan Zhang and
Jun Zhou^,

School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

^* Corresponding author
^* Corresponding author

Received: August 2020

Revised: January 2021

Early access: March 2021

Published: April 2021

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Abstract

To understand the characteristics of dynamical behavior especially the kinetic evolution for logarithmic nonlinearity, we aim to study a sixth-order Boussinesq equation with logarithmic nonlinearity in a bounded domain $ \Omega\subset \mathbb{R}^n $ ($ n\geq1 $ is an integer) with smooth boundary $ \partial\Omega $, where the dispersive and the strong damping are taken into account. Based on the Faedo-Galërkin method, the logarithmic Sobolev inequality, and the potential well method, the main ingredient of this paper is to construct several conditions for initial data leading to the solution global existence or infinite time blow-up, and to study the polynomial decay and the exponential decay of the energy of the system.

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Mathematics Subject Classification: Primary: 35B30; Secondary: 35B40, 35L30.

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