On the global existence of solution to one-dimensional fourth order nonlinear Sobolev type equations

Abstract: We prove the global existence and uniqueness of a classical solution to initial boundary value problem for a class of Sobolev type equations under the Dirichlet boundary conditions. This class of evolution equations covers the well-known viscous Cahn–Hilliard equation and the viscous Camassa–Holm equation. [ABSTRACT FROM AUTHOR]