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• W4323865881 abstract "We study the long-time behavior of solutions to quasilinear doubly degenerate parabolic problems of fourth order. The equations model, for instance, the dynamic behavior of a non-Newtonian thin-film flow on a flat impermeable bottom and with zero contact angle. We consider a shear-rate dependent fluid the rheology of which is described by a constitutive power law or Ellis law for the fluid viscosity. In all three cases, positive constants (i.e., positive flat films) are the only positive steady-state solutions. Moreover, we can give a detailed picture of the long-time behavior of solutions with respect to the -norm. In the case of shear-thickening power-law fluids, one observes that solutions which are initially close to a steady state converge to equilibrium in finite time. In the shear-thinning power-law case, we find that steady states are polynomially stable in the sense that, as time tends to infinity, solutions which are initially close to a steady state converge to equilibrium at rate for some . Finally, in the case of an Ellis fluid, steady states are exponentially stable in ." @default.
• W4323865881 created "2023-03-11" @default.
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• W4323865881 date "2023-03-10" @default.
• W4323865881 modified "2023-10-17" @default.
• W4323865881 title "Long-Time Behavior and Stability for Quasilinear Doubly Degenerate Parabolic Equations of Higher Order" @default.
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• W4323865881 doi "https://doi.org/10.1137/22m1491137" @default.
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