Department of Mathematics2024-11-0920130022-248810.1063/1.47987862-s2.0-84877665732https://hdl.handle.net/20.500.14288/3040We study initial boundary value problems for the unstable convective Cahn-Hilliard (CH) equation, i.e., the Cahn Hilliard equation whose energy integral is not bounded below. It is well-known that without the convective term, the solutions of the unstable CH equation ?t u + ? 4xu + ?2x(|u|pu) = 0 may blow up in ?nite time for anyp > 0. In contrast to that, we show that the presence of the convective term u?xuin the Cahn-Hilliard equation prevents blow up at least for 0 < p <49. We alsoshow that the blowing up solutions still exist if p is large enough (p ? 2). The related equations like Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard equation, are also considered.pdfMathematical physicsJournal Article1089-7658https://doi.org/10.1063/1.4798786318551900002Q3NOIR00117