Global existence and asymptotic behavior of a solution of Cauchy problem for a viscous Cahn–Hilliard type equation

Abstract

We consider the existence, both locally and globally in time and the asymptotic behavior of solution of Cauchy problem for a viscous Cahn-Hilliard type equation. Under rather mild conditions on nonlinear term and initial data we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the problem is globally well-posed. Finally, under certain conditions, we prove that the global solution decays exponentially to zero as tends to infinity.