In this paper we investigate the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential.By the energy method and the theory of Campanato spaces,...In this paper we investigate the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential.By the energy method and the theory of Campanato spaces,we prove the existence and the uniqueness of classical solutions in 3-dimensional space.展开更多
In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann bo...In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann boundary condition (see <a href="#ref1">[1]</a>). By the semi-group theory, we prove the existence and uniqueness of the solution for the model and thanks to a duality method we do the numerical analysis of the problem. We finish our work by doing numerical simulations to validate our theoretical results.展开更多
The issue of mesh-dependence emerges when the conventional continuum damage model is applied to handling the softening behavior. In order to circumvent the mesh-dependence, the non-local theory is introduced into the ...The issue of mesh-dependence emerges when the conventional continuum damage model is applied to handling the softening behavior. In order to circumvent the mesh-dependence, the non-local theory is introduced into the conventional damage model and the finite element formulas are derived for two-dimensional gradient-enhanced damage model. A new element is proposed in which the basic unknown quantities are displacement, non-local equivalent strain and the gradient of non-local equivalent strain. The element and constitutive equation proposed in this article are added to the finite element software ABAQUS through user subroutine UEL. Numerical results show that the gradient-enhanced damage model can eliminate the mesh-dependence and is effective for dealing with the issue of softening behavior.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.11001103)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.200801831002)+1 种基金the China Postdoctoral Science Foundation (Grant No.20100481229)the Fundamental Research Funds for the Central Universities
文摘In this paper we investigate the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential.By the energy method and the theory of Campanato spaces,we prove the existence and the uniqueness of classical solutions in 3-dimensional space.
文摘In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann boundary condition (see <a href="#ref1">[1]</a>). By the semi-group theory, we prove the existence and uniqueness of the solution for the model and thanks to a duality method we do the numerical analysis of the problem. We finish our work by doing numerical simulations to validate our theoretical results.
文摘The issue of mesh-dependence emerges when the conventional continuum damage model is applied to handling the softening behavior. In order to circumvent the mesh-dependence, the non-local theory is introduced into the conventional damage model and the finite element formulas are derived for two-dimensional gradient-enhanced damage model. A new element is proposed in which the basic unknown quantities are displacement, non-local equivalent strain and the gradient of non-local equivalent strain. The element and constitutive equation proposed in this article are added to the finite element software ABAQUS through user subroutine UEL. Numerical results show that the gradient-enhanced damage model can eliminate the mesh-dependence and is effective for dealing with the issue of softening behavior.
