Well-Posedness Of Solutions To A Class Of Generalized Cahn-Hilliard Equations

In this thesis,the well-posedness of solutions to a class of generalized CahnHilliard equations with proliferation term in a bounded domain are studied.These equations are mainly used to describe a class of diffusion phenomenas in physics and biology.In this thesis,the generalized Cahn-Hilliard equations with different nonlinear terms are studied under the condition that the proliferation term satisfies more general assumptions,and the well-posedness of the weak solutions to the equations with Neumann boundary condition are obtained by using the standard Galerkin scheme,a priori estimate and Aubin-Lions compactness lemma.Moreover,the relevant regularity and global property of the solutions are proved.In the first chapter,the significance of the Cahn-Hilliard equation and the related generalized Cahn-Hilliard equations and the existing main research results are introduced.In the second chapter,we introduce the related function spaces,theorems,lemmas and important inequalities.In the third chapter,we study the well-posedness and correlation regularity of weak solutions under the condition that the nonlinear term 1)()and the proliferation term 2)()satisfy more general nonlinear conditions.In the fourth chapter,under the constraint that the nonlinear term 1)()is logarithmic function and the proliferation term 2)()satisfies more general nonlinear conditions,the adaptability of the weak solution is studied,and the globality of the solution is proved under appropriate assumptions.