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Weak Solutions to the Cahn—Hilliard Equation with Degenerate Diffusion Mobility in ℝN

  • Ji Hui WuEmail author
  • Lei LuEmail author
Article

Abstract

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.

Keywords

Degenerate non-degenerate viscous convergence 

MR(2010) Subject Classification

35K55 35B40 

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Notes

Acknowledgements

The authors are grateful to reviewers and for their time and comments.

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© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.College of Mathematics, Physics and StatisticsShanghai University of Engineering ScienceShanghaiP. R. China
  2. 2.College of SciencesShanghai UniversityShanghaiP. R. China
  3. 3.College of Mechanical EngineeringBeijing University of TechnologyBeijingP. R. China

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