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arXiv · 2511.04947

Asymptotic Stability and the Forcing Term: An Analysis of Non-Newtonian Thin-Film Flows

Jinhong Zhao·Bin Guo
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Abstract

We study a class of fourth-order quasilinear degenerate parabolic equations under both time-and space-dependent and time-and space-independent forces, modeling non-Newtonian thin-film flow over a solid surface in the "complete wetting" regime. By analyzing the quantitative properties of solutions to non-autonomous differential inequalities and employing refined integral estimates, we derive two-sided convergence rate estimates for the solution. Numerical simulations are further provided to illustrate the consistency of our main results with the observed physical phenomena.

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Jinhong Zhao, Bin Guo. 2025-11-07. Asymptotic Stability and the Forcing Term: An Analysis of Non-Newtonian Thin-Film Flows. https://arxiv.org/abs/2511.04947

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