Research Announcement: Finite-time Blow Up and Long-wave Unstable Thin Film Equations

Details Research Announcement: Finite-time Blow Up and Long-wave Unstable Thin Film Equations Research Announcement: Finite-time Blow Up and Long-wave Unstable Thin Film Equations

2010-08-02

arxiv.org/abs/1008.0385v1

Physics

Mathematical Physics

59 pages, 1 figure

Scientific paper

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 $a_1 >0$. The existence and finite speed of propagation results extend those of [Comm Pure Appl Math 51:625--661, 1998]. For $0

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