Finite-time blow up and long-wave unstable thin-film equations

Start: 10/30/2013 - 1:15pm
End  : 10/30/2013 - 2:15pm

Applied Math Seminar

Marina Chugunova (CGU)


We study short-time existence,  long-time existence, finite speed of propagation, and finite-time blow-up of non-negative solutions for long-wave unstable thin-film equations $ h_t = -(h^n h_{xxx})_x - (h^m h_x)_x $ with $ n $>0. We consider a large range of exponents $ (n,m) $ within the super-critical $ m $>$ n+2 $ and critical $ m+2 $ regimes. For the  initial data with negative energy we prove that the solution blows up in finite time with its $ H^1 $ and $ L^\infty $ norms going to infinity. [In collaboration with Mary C. Pugh and Roman M. Taranets]


Davidson Lecture Hll