Rocky Mountain Journal of Mathematics

The Cauchy problem for the degenerate convective Cahn-Hilliard equation

Aibo Liu and Changchun Liu

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Abstract

In this paper, we study the degenerate convective Cahn-Hilliard equation, which is a special case of the general convective Cahn-Hilliard equation with $M(u,\nabla u)=diag(0,1,\ldots ,1)$. We obtain the uniform a priori decay estimates of a solution by use of the long-short wave method and the frequency decomposition method. We prove the existence of the unique global classical solution with small initial data by establishing the uniform estimates of the solution. Decay estimates are also discussed.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 8 (2018), 2595-2623.

Dates
First available in Project Euclid: 30 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1546138823

Digital Object Identifier
doi:10.1216/RMJ-2018-48-8-2595

Mathematical Reviews number (MathSciNet)
MR3894995

Zentralblatt MATH identifier
06999276

Subjects
Primary: 35K25: Higher-order parabolic equations
Secondary: 35A09: Classical solutions 35K59: Quasilinear parabolic equations

Keywords
Convective Cahn-Hilliard equation frequency decomposition existence Green's function method

Citation

Liu, Aibo; Liu, Changchun. The Cauchy problem for the degenerate convective Cahn-Hilliard equation. Rocky Mountain J. Math. 48 (2018), no. 8, 2595--2623. doi:10.1216/RMJ-2018-48-8-2595. https://projecteuclid.org/euclid.rmjm/1546138823


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