7 research outputs found
Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials
We study initial boundary value problems for the convective Cahn-Hilliard
equation \Dt u +\px^4u +u\px u+\px^2(|u|^pu)=0. It is well-known that without
the convective term, the solutions of this equation may blow up in finite time
for any . In contrast to that, we show that the presence of the convective
term u\px u in the Cahn-Hilliard equation prevents blow up at least for
. We also show that the blowing up solutions still exist if is
large enough (). The related equations like
Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard
equation, are also considered