Weak Solutions to the Cahn—Hilliard Equation with Degenerate Diffusion Mobility in ℝN
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) = um (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.
KeywordsDegenerate non-degenerate viscous convergence
MR(2010) Subject Classification35K55 35B40
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The authors are grateful to reviewers and for their time and comments.
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