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### Open Access Journals

CPAA

In this paper, we study the time periodic solution of a
sixth order nonlinear parabolic equation, which
arises in oil-water-surfactant mixtures. Based on Leray-Schauder's
fixed point theorem and Campanato spaces, we prove the existence of time-periodic solutions in two space dimensions.

CPAA

In this paper, we study a fourth order degenerate parabolic
equation, which arises in epitaxial growth of nanoscale thin films. We establish the existence of weak solutions, based on the
uniform estimates for the approximate solutions. The nonnegativity and the finite
speed of propagation of perturbations of solutions are also discussed.

EECT

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.

EECT

In this paper, we discuss the existence of the periodic solutions of a Cahn-Hillard/Allen-Cahn equation which is introduced as a simplification of multiple microscopic mechanisms model in cluster interface evolution. Based on the Schauder type a priori estimates, which here will be obtained by means of a modified Campanato space, we prove the existence of time-periodic solutions in two space dimensions. The uniqueness of solutions is also discussed.

CPAA

In this paper, we consider an initial-boundary problem for a fourth-order
nonlinear parabolic
equations. The problem as a model shares the scaling properties of the thin film
equation, or as a model
arises in epitaxial growth of nanoscale thin films.
Our approach lies in the
combination of the energy techniques with some methods based on the framework of
Campanato spaces. Based on the
uniform estimates for the approximate solutions,
we establish the existence of weak solutions.

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