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Weak Solutions to the Cahn-Hilliard Equation with Degenerate Diffusion Mobility in R^N
Ji; Hui; WU; Lei; LU College; of; Mathematics; Physics; and; Statistics; Shanghai; University; of; Engineering; Science; Shanghai; 201620; P.R.China; College; of; Sciences; Shanghai; University; Shanghai; 200444; P.R.China; College; of; Mechanical; Engineering; Beijing; University; of; Technology; Beijing; 100124; P.R.China
- degenerate
- viscous
- convergence
摘要：This paper is concerned with a popular form of Cahn-Hilliard equation which plays an important role in understanding the evolution of phase separation. We get the existence and regularity of a weak solution to nonlinear parabolic, fourth order Cahn-Hilliard equation with degenerate mobility M(u)= u^m(1-u)^m which is allowed to vanish at 0 and 1. The existence and regularity of weak solutions to the degenerate Cahn-Hilliard equation are obtained by getting the limits of Cahn-Hilliard equation with non-degenerate mobility. We explore the initial value problem with compact support and obtain the local non-negative result. Further, the above derivation process is also suitable for the viscous Cahn–Hilliard equation with degenerate mobility.
- degenerate
- viscous
- convergence
摘要：This paper is concerned with a popular form of Cahn-Hilliard equation which plays an important role in understanding the evolution of phase separation. We get the existence and regularity of a weak solution to nonlinear parabolic, fourth order Cahn-Hilliard equation with degenerate mobility M(u)= u^m(1-u)^m which is allowed to vanish at 0 and 1. The existence and regularity of weak solutions to the degenerate Cahn-Hilliard equation are obtained by getting the limits of Cahn-Hilliard equation with non-degenerate mobility. We explore the initial value problem with compact support and obtain the local non-negative result. Further, the above derivation process is also suitable for the viscous Cahn–Hilliard equation with degenerate mobility.
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