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.

For 0 < n < 2 we prove the existence of a nonnegative, compactly supported, strong solution on the line that blows up in finite time. The construction requires that the initial data be nonnegative, compactly supported, and have negative energy. The blow-up is proven for a large range of (n,m) exponents and extends the results of [Indiana Univ Math J 49:1323-1366, 2000].