Advances in Differential Equations

Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability

Peter W. Bates, E. Norman Dancer, and Junping Shi

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Abstract

It is proved that the Cahn-Hilliard equation on a smooth domain possesses solutions which have spike layers localizing where the mean curvature of the boundary of the domain has nondegenerate critical points. Solutions of this type can be found with any average value which lies in the metastable region. It is also shown that these solutions have Morse indices at least equal to the number of spikes.

Article information

Source
Adv. Differential Equations, Volume 4, Number 1 (1999), 1-69.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366291798

Mathematical Reviews number (MathSciNet)
MR1667283

Zentralblatt MATH identifier
1157.35407

Subjects
Primary: 35K60: Nonlinear initial value problems for linear parabolic equations
Secondary: 35B25: Singular perturbations 35B40: Asymptotic behavior of solutions 58E50: Applications

Citation

Bates, Peter W.; Dancer, E. Norman; Shi, Junping. Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability. Adv. Differential Equations 4 (1999), no. 1, 1--69. https://projecteuclid.org/euclid.ade/1366291798


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