Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.
In this paper,blow-up phenomena of solutions to a class of parabolic equations for porous media with nonlocal source terms cross-coupled under Dirichlet and Neumann boundary conditions are studied.The differential ine...In this paper,blow-up phenomena of solutions to a class of parabolic equations for porous media with nonlocal source terms cross-coupled under Dirichlet and Neumann boundary conditions are studied.The differential inequality techniques are used to obtain the lower bounds on the blow up time of the equation set under two different boundary conditions.展开更多
In the paper,the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied.by cons...In the paper,the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied.by constructing the upper and lower solutions with the ordinary differential equation as well as introducing the comparison theorem,the global existence and finite time blow-up of the solution of parabolic equations of porous media coupled by the power function and the logarithm function are obtained.The differential inequality technique is used to obtain the lower bounds on the blow up time of the above equations under Dirichlet and Neumann boundaryconditions.展开更多
This paper is the continuation of [2]. Some typical behaviors of weak solutions of layered porous media equations with boundary conditions will be discussed in this paper. For example, asymptotically, the saturated re...This paper is the continuation of [2]. Some typical behaviors of weak solutions of layered porous media equations with boundary conditions will be discussed in this paper. For example, asymptotically, the saturated regions can appear only either hear the layered interface, or near the boundaries. The necessary and sufficient conditions for the occurrence of such phenomena will be given.展开更多
The Richards equation models the water flow in a partially saturated underground porous medium under the surface.When it rains on the surface,boundary conditions of Signorini type must be considered on this part of th...The Richards equation models the water flow in a partially saturated underground porous medium under the surface.When it rains on the surface,boundary conditions of Signorini type must be considered on this part of the boundary.The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler's scheme in time and finite elements in space.The convergence of this discretization leads to the well-posedness of the problem.展开更多
In this paper, let(M~n, g) be an n-dimensional complete Riemannian manifold with the mdimensional Bakry–mery Ricci curvature bounded below. By using the maximum principle, we first prove a Li–Yau type Harnack differ...In this paper, let(M~n, g) be an n-dimensional complete Riemannian manifold with the mdimensional Bakry–mery Ricci curvature bounded below. By using the maximum principle, we first prove a Li–Yau type Harnack differential inequality for positive solutions to the parabolic equation u= LF(u)=ΔF(u)-f·F(u),on compact Riemannian manifolds Mn, where F∈C~2(0, ∞), F>0 and f is a C~2-smooth function defined on M~n. As application, the Harnack differential inequalities for fast diffusion type equation and porous media type equation are derived. On the other hand, we derive a local Hamilton type gradient estimate for positive solutions of the degenerate parabolic equation on complete Riemannian manifolds. As application, related local Hamilton type gradient estimate and Harnack inequality for fast dfiffusion type equation are established. Our results generalize some known results.展开更多
In this article, the bounding surfaces of channels were modeled by Bayesian stochastic simulation, which is a boundary-valued problem with observed valley erosion thickness at the locations of wells （hard data）. In ...In this article, the bounding surfaces of channels were modeled by Bayesian stochastic simulation, which is a boundary-valued problem with observed valley erosion thickness at the locations of wells （hard data）. In this study, it was assumed that the cross-section of the channel shows a parabolic shape, and the case that the vertical well and the horizontal well are located in the channel was considered. Peaceman＇s equations were modified to simultaneously solve both the vertical well problem and the horizontal well problem. In porous media, a 3D fluid equation was solved with iteration in the spatial domain, which had channels, vertical wells, and horizontal wells. As an example, the spatial distributions of pressure were calculated for channel reservoirs containing vertical and horizontal wells.展开更多
基金Project supported by the Tianyuan Foundation of National Natural Science of China(No.11126079)the China Postdoctoral Science Foundation(No.2013M530559)the Fundamental Research Funds for the Central Universities(No.CDJRC10100011)
文摘Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.
基金Supported by Natural Science Basic Research Project of Shaanxi Province(2019JM-534)Soft Science Project of Shaanxi Province(2019KRM169)+3 种基金Project on Higher Education Teaching Reform of Xi’an International University(2019B36)Project of Qi Fang Education Research Institute of Xi’an International University(21mjy07)Special Project Support of the 14th Five Year Plan of the China Association of Higher Education(21DFD04)the Youth Innovation Team of Shaanxi Universities
文摘In this paper,blow-up phenomena of solutions to a class of parabolic equations for porous media with nonlocal source terms cross-coupled under Dirichlet and Neumann boundary conditions are studied.The differential inequality techniques are used to obtain the lower bounds on the blow up time of the equation set under two different boundary conditions.
基金supported by Natural Science Basic Research Project of Shaanxi Province(2019JM-534)Soft Science Project of Shaanxi Province(2019KRM169)+3 种基金Project of Qi Fang Education Research Institute of Xian International University(21mjy07)Special project support of the 14th five year plan of the China Association of Higher Education(Topic name:Research on the adaptability of specialty structure and industrial structure of Local Universities-a case study of Shaanxi Province,No:21DFD04)2021 youth innovation team construction scientific research plan project of Shaanxi Provincial Department of Education(21JP105)The Youth Innovation Team of Shaanxi Universities,Shaanxi educational science"14th five year plan"project(SGH21Y0308).
文摘In the paper,the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied.by constructing the upper and lower solutions with the ordinary differential equation as well as introducing the comparison theorem,the global existence and finite time blow-up of the solution of parabolic equations of porous media coupled by the power function and the logarithm function are obtained.The differential inequality technique is used to obtain the lower bounds on the blow up time of the above equations under Dirichlet and Neumann boundaryconditions.
文摘This paper is the continuation of [2]. Some typical behaviors of weak solutions of layered porous media equations with boundary conditions will be discussed in this paper. For example, asymptotically, the saturated regions can appear only either hear the layered interface, or near the boundaries. The necessary and sufficient conditions for the occurrence of such phenomena will be given.
文摘The Richards equation models the water flow in a partially saturated underground porous medium under the surface.When it rains on the surface,boundary conditions of Signorini type must be considered on this part of the boundary.The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler's scheme in time and finite elements in space.The convergence of this discretization leads to the well-posedness of the problem.
基金Supported by Universities Natural Science Foundation of Anhui Province(Grant No.KJ2016A310)
文摘In this paper, let(M~n, g) be an n-dimensional complete Riemannian manifold with the mdimensional Bakry–mery Ricci curvature bounded below. By using the maximum principle, we first prove a Li–Yau type Harnack differential inequality for positive solutions to the parabolic equation u= LF(u)=ΔF(u)-f·F(u),on compact Riemannian manifolds Mn, where F∈C~2(0, ∞), F>0 and f is a C~2-smooth function defined on M~n. As application, the Harnack differential inequalities for fast diffusion type equation and porous media type equation are derived. On the other hand, we derive a local Hamilton type gradient estimate for positive solutions of the degenerate parabolic equation on complete Riemannian manifolds. As application, related local Hamilton type gradient estimate and Harnack inequality for fast dfiffusion type equation are established. Our results generalize some known results.
基金Project supported by the Scientific Research Common Program of Beijing Municipal Commission of Education (Grant No: KM200510015003)
文摘In this article, the bounding surfaces of channels were modeled by Bayesian stochastic simulation, which is a boundary-valued problem with observed valley erosion thickness at the locations of wells （hard data）. In this study, it was assumed that the cross-section of the channel shows a parabolic shape, and the case that the vertical well and the horizontal well are located in the channel was considered. Peaceman＇s equations were modified to simultaneously solve both the vertical well problem and the horizontal well problem. In porous media, a 3D fluid equation was solved with iteration in the spatial domain, which had channels, vertical wells, and horizontal wells. As an example, the spatial distributions of pressure were calculated for channel reservoirs containing vertical and horizontal wells.
