In this paper we consider the viscous Cahn-Hilliard equation with spatial dimension n ≤ 5, and established global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initia...In this paper we consider the viscous Cahn-Hilliard equation with spatial dimension n ≤ 5, and established global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initial data.展开更多
The motivation of this paper is to systematically study how the inertial term affects the behavior of the solution of the Cahn-Hilliard equation.When there is an inertial term,the equation becomes a parabolic-hyperbol...The motivation of this paper is to systematically study how the inertial term affects the behavior of the solution of the Cahn-Hilliard equation.When there is an inertial term,the equation becomes a parabolic-hyperbolic one.To overcome the difficulties from large perturbation and the hyperbolicity,a few elaborate energy estimates should be given,which are based on choosing suitable space of the smooth solution,even some inequalites in negative Sobolev space.More precisely,for 1-dimensional(1D)non-viscous case and 1D,2D,and 3D viscous case,the global existence of the smooth solutions are given.Moreover,several blow-up results are established by using the convex method.The results exhibit the interplay between the viscosity and the inertial term for the behavior of the smooth solution.展开更多
This paper is devoted to viscous Cahn-Hiliiard equation with concentration dependent mobility. Some results on the existence, uniqueness and large time behavior are established.
This article is devoted to the discussion of large time behaviour of solutions for viscous Cahn-Hilliard equation with spatial dimension n 〈 5. Some results on global existence of weak solutions for small initial val...This article is devoted to the discussion of large time behaviour of solutions for viscous Cahn-Hilliard equation with spatial dimension n 〈 5. Some results on global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initial value are established.展开更多
基金The NSF (10125107) of China and partially supported by a Specific Foundation for Ph.D Specialities of Educational Department of China.
文摘In this paper we consider the viscous Cahn-Hilliard equation with spatial dimension n ≤ 5, and established global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initial data.
基金National Natural Science Foundation of China(No.11971100)Fundamental Research Funds for the Central Universities,China(No.2232019D3-43)
文摘The motivation of this paper is to systematically study how the inertial term affects the behavior of the solution of the Cahn-Hilliard equation.When there is an inertial term,the equation becomes a parabolic-hyperbolic one.To overcome the difficulties from large perturbation and the hyperbolicity,a few elaborate energy estimates should be given,which are based on choosing suitable space of the smooth solution,even some inequalites in negative Sobolev space.More precisely,for 1-dimensional(1D)non-viscous case and 1D,2D,and 3D viscous case,the global existence of the smooth solutions are given.Moreover,several blow-up results are established by using the convex method.The results exhibit the interplay between the viscosity and the inertial term for the behavior of the smooth solution.
基金Qutstanding Youth Foundation (10125107) of China a Key Grant of the Ministry of Science and Technologies.
文摘This paper is devoted to viscous Cahn-Hiliiard equation with concentration dependent mobility. Some results on the existence, uniqueness and large time behavior are established.
文摘This article is devoted to the discussion of large time behaviour of solutions for viscous Cahn-Hilliard equation with spatial dimension n 〈 5. Some results on global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initial value are established.
