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

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  • Qingqing Peng

    (Huazhong University of Science and Technology
    Huazhong University of Science and Technology)

  • Zhifei Zhang

    (Huazhong University of Science and Technology
    Huazhong University of Science and Technology)

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.

Suggested Citation

  • Qingqing Peng & Zhifei Zhang, 2025. "Stabilization and blow-up for a class of weakly damped Kirchhoff plate equation with logarithmic nonlinearity," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(2), pages 711-727, June.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:2:d:10.1007_s13226-023-00518-8
    DOI: 10.1007/s13226-023-00518-8
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    References listed on IDEAS

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    1. Li, Fushan & Gao, Qingyong, 2016. "Blow-up of solution for a nonlinear Petrovsky type equation with memory," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 383-392.
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