Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials
Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials
We 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 \documentclass[12pt]{minimal}\begin{document}$\partial _tu +\partial _{x}^4u +\partial _{x}^2(|u|^pu)=0$\end{document}∂tu+∂x4u+∂x2(|u|pu)=0 may blow up in …