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Weak Solutions for the Cahn–Hilliard Equation with Degenerate Mobility

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Abstract

In this paper, we study the well-posedness of Cahn–Hilliard equations with degenerate phase-dependent diffusion mobility. We consider a popular form of the equations which has been used in phase field simulations of phase separation and microstructure evolution in binary systems. We define a notion of weak solutions for the nonlinear equation. The existence of such solutions is obtained by considering the limits of Cahn–Hilliard equations with non-degenerate mobilities.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, USA

    Shibin Dai

  2. Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA

    Qiang Du

Authors
  1. Shibin Dai
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  2. Qiang Du
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Correspondence to Shibin Dai.

Additional information

Communicated by I. Fonseca

S. Dai is supported in part by US NSF Grant DMS-1411438. Q. Du is supported in part by US NSF Grant DMS-1318586.

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Dai, S., Du, Q. Weak Solutions for the Cahn–Hilliard Equation with Degenerate Mobility. Arch Rational Mech Anal 219, 1161–1184 (2016). https://doi.org/10.1007/s00205-015-0918-2

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  • DOI: https://doi.org/10.1007/s00205-015-0918-2

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