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تسجيل مستخدم جديدNonnegative solutions for a long-wave unstable thin film equation with convection
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We consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surface of a rotating horizontal cylinder in the presence of gravity. The parameters involved determine a rich variety of qualitatively different flows. Depending on the initial data and the parameter values, we prove the existence of nonnegative periodic weak solutions. In addition, we prove that these solutions and their gradients cannot grow any faster than linearly in time; there cannot be a finite-time blow-up. Finally, we present numerical simulations of solutions.
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In this technical report, we consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surface of a rotating horizontal cylinder in the p
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We study short--time existence, long--time existence, finite speed of propagation, and finite--time blow--up of nonnegative solutions for long-wave unstable thin film equations $h_t = -a_0(h^n h_{xxx})_x - a_1(h^m h_x)_x$ with $n>0$, $a_0 > 0$, and $
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