Cauchy problem for a sixth order Cahn-Hilliard type equation with inertial term

Aibo  Liu; Changchun Liu

doi:10.3934/eect.2015.4.315

Article Contents

2015, Volume 4, Issue 3: 315-324. Doi: 10.3934/eect.2015.4.315

This issue Previous Article An Ingham--Müntz type theorem and simultaneous observation problems Next Article Exact internal controllability for the wave equation in a domain with oscillating boundary with Neumann boundary condition

Cauchy problem for a sixth order Cahn-Hilliard type equation with inertial term

Aibo Liu^1, and
Changchun Liu^2,

1.
Department of Mathematics, Jilin University, Changchun 130012
2.
Department of Mathematics, and Key Laboratory of Symbolic Computation, and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012

Received: September 30, 2014

Revised: February 28, 2015

Published: August 2015

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Abstract

In this paper, we consider the Cauchy problem of a sixth order Cahn-Hilliard equation with the inertial term, \begin{eqnarray*} ku_{t t} + u_t - \Delta^3 u - \Delta(-a(u) \Delta u -\frac{a'(u)}2|\nabla u|^2 + f(u))=0. \end{eqnarray*} Based on Green's function method together with energy estimates, we get the global existence and optimal decay rate of solutions.

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Mathematics Subject Classification: Primary: 35L30, 35L77; Secondary: 35B40.

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