Evolution Equations and Control Theory (EECT)

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

Pages: 315 - 324, Volume 4, Issue 3, September 2015      doi:10.3934/eect.2015.4.315

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Aibo Liu - Department of Mathematics, Jilin University, Changchun 130012, China (email)
Changchun Liu - Department of Mathematics, and Key Laboratory of Symbolic Computation, and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China (email)

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.

Keywords:  Sixth order Cahn-Hilliard, existence, optimal decay rate, inertial term.
Mathematics Subject Classification:  Primary: 35L30, 35L77; Secondary: 35B40.

Received: October 2014;      Revised: March 2015;      Available Online: September 2015.