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2018 The Cauchy problem for the degenerate convective Cahn-Hilliard equation
Aibo Liu, Changchun Liu
Rocky Mountain J. Math. 48(8): 2595-2623 (2018). DOI: 10.1216/RMJ-2018-48-8-2595

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.

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Aibo Liu. Changchun Liu. "The Cauchy problem for the degenerate convective Cahn-Hilliard equation." Rocky Mountain J. Math. 48 (8) 2595 - 2623, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2595

Information

Published: 2018
First available in Project Euclid: 30 December 2018

zbMATH: 06999276
MathSciNet: MR3894995
Digital Object Identifier: 10.1216/RMJ-2018-48-8-2595

Subjects:
Primary: 35K25
Secondary: 35A09, 35K59

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 8 • 2018
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