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

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.

preprint2026arXivOpen access
Jinhong ZhaoBin Guo
math.APmath-phmath.MPmath.NANumerical Analysis
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Open access2 authors5 topics
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Jinhong ZhaoBin Guo

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