Stabilization and blow-up for a class of weakly damped Kirchhoff plate equation with logarithmic nonlinearity

Qingqing Peng () and Zhifei Zhang ()
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Qingqing Peng: Huazhong University of Science and Technology
Zhifei Zhang: Huazhong University of Science and Technology

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 2, 711-727

Abstract: Abstract In this paper, we consider the initial value problem for weakly damped Kirchhoff plate equation with logarithmic nonlinearity in a bounded domain. We investigate the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under initial energy less than the depth of the potential well and some appropriate conditions. Moreover, we derive the finite time blow up of the weak solution with upper bounded initial energy.

Keywords: Plate equation; Logarithmic nonlinear; Weakly damping; Finite time blow-up; Polynomial and exponential decay (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00518-8

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