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<p>This study examines the continuous dependence on initial data of a damped plate system that includes the <i>p</i>-Laplacian operator and logarithmic source terms. By applying energy decay estimates [1], we derive conclusions regarding the continuous dependence of the global solution on initial data and the coefficients associated with strong damping terms and coupled velocity terms. To estimate the continuous dependence on initial conditions, we adopt a novel approach developed by Han <i>et al.</i> [2], which enhances our understanding of this dependence. For the estimation of logarithmic terms, we introduce a method distinct from conventional approaches, thereby obtaining more refined results. This study contributes to the theoretical analysis of nonlinear partial differential equations and provides new insights into handling logarithmic source terms in damped plate systems.</p>

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The continuous dependence on initial data of a p-Laplacian plate system with strong dampings and logarithmic nonlinearities

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Yifei Dai

摘要

This study examines the continuous dependence on initial data of a damped plate system that includes the p-Laplacian operator and logarithmic source terms. By applying energy decay estimates [1], we derive conclusions regarding the continuous dependence of the global solution on initial data and the coefficients associated with strong damping terms and coupled velocity terms. To estimate the continuous dependence on initial conditions, we adopt a novel approach developed by Han et al. [2], which enhances our understanding of this dependence. For the estimation of logarithmic terms, we introduce a method distinct from conventional approaches, thereby obtaining more refined results. This study contributes to the theoretical analysis of nonlinear partial differential equations and provides new insights into handling logarithmic source terms in damped plate systems.