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Global existence and asymptotic behavior of solutions to Cahn-Hilliard equation with inertial term. (English) Zbl 1250.35146
Summary: We investigate the Cauchy problem for Cahn-Hilliard equation with inertial term in n-dimensional space. Based on the decay estimate of solutions to the corresponding linear equation, we define a solution space. Under small condition on the initial value, we prove the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces by the contraction mapping principle.
MSC:
35L76Semilinear higher-order hyperbolic equations
35L30Higher order hyperbolic equations, initial value problems
35B40Asymptotic behavior of solutions of PDE