Convective Porous Medium Systems with Nonlinear Forcing at the Boundary

This paper deals with the global positive solutions of convective porous medium systems with nonlinear forcing at the boundary. Necessary and sufficient conditions on the global existence of all positive solutions are obtained.     

Fujita Exponent for Porous Medium Equation with Convection and Nonlinear Boundary Condition

This paper is concerned with the critical exponent of the porous medium equation with convection and nonlinear boundary condition. It is shown that the coefficient of the lower order term is an important factor that determines the critical exponent.     

具对流和非线性边值条件渗流方程的Fujita指标

This paper is concerned with the critical exponent of the porous medium equation with convection and nonlinear boundary condition. It is shown that the coefficient of the lower order term is an important factor that determines the critical exponent.     

Blow-up of Solutions to Porous Medium Equations with a Nonlocal Boundary Condition and a Moving Localized Source

This paper is devoted to the blow-up properties of solutions to the porous medium equations with a nonlocal boundary condition and a moving localized source.Conditions for the existence of global or bl...     

Sources Acting on the Free Boundary of a Porous Biot Medium and Reflection on This Boundary

A homogeneous isotropic porous Biot half-space z 0 with free boundary z = 0 is considered. This half-space is excited by point sources situated on the boundary z = 0 and applied to the elastic phase. The following four sources are considered: (1) a normal force, (2) a center of tangent forces, (3) a center of rotation, and (4) a tangent force. For all these sources, the wave fields are established. Relationships between the wave fields in a porous medium and the respective wave fields in an elastic medium are investigated. The reflection coefficients on the free boundary of the porous Biot half-space are determined and studied. Bibliography: 11 titles.     

具有微极弹性构架的流体-饱和多孔固体中波在边界面处的传播

通过研究匀质非黏性液体半空间和微极流体饱和多孔固体半空间交界面处平面波的反射与透射,得到不同角度入射波的反射和透射系数.计算出反射波与透射波的振幅比数值,并用图表示出微极性和多孔性对反射和透射的影响.最后根据公式对一些特例进行了推导.     

Evolution of a Condensation Surface in a Porous Medium near the Instability Threshold

We consider the dynamics of a narrow band of weakly unstable and weakly nonlinear perturbations of a plane phase transition surface separating regions of soil saturated with water and with humid air; during transition to instability, the existing stable position of the phase transition surface is assumed to be sufficiently close to another phase transition surface that arises as a result of a turning point bifurcation. We show that such perturbations are described by a Kolmogorov–Petrovskii–Piskunov type equation.     

Parabolic Free Boundary Problems Arising in Porous Medium Combustion

A parabolic partial differential equation approximating theevolution of temperature in highly exothermic porous-mediumcombustion at low driving velocities is examined. The equationis of reaction-diffusion type with a reaction term which isdiscontinuous as a function of the dependent variable. Firstly the variation of the steady solution set with the scaledheat of the reaction is described and the related time-dependentbehaviour analysed. The stability results follow from characterizingthe ends of the solution branch and fold points explicitly anddeducing global stability results about the whole of the continuoussolution branch. The results are used to indicate the parameterregimes and temporal scales on which the small driving velocityapproximation ceases to be valid. Secondly the behaviour of the discontinuous partial differentialequation is compared with that of a continuous equation whichit approximates. This provides justification for the approximationof reaction terms possessing steep gradients by discontinuousfunctions; the large activation energy limit in porous-mediumcombustion involves such a process.     

On Thermal Boundary Layer in a Viscous Non-Newtonian Medium

Doklady Mathematics - An existence and uniqueness theorem for a classical solution to the system of equations describing thermal boundary layers in viscous media with the Ladyzhenskaya rheological...     

On Vector Helmholtz Equation with a Coupling Boundary Condition

The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown.In this paper, we study the vector Helmholtz problem in domains of both C~(1,1)and Lipschitz.We es- tablish a rigorous variational analysis such as equivalence,existence and uniqueness. And we propose finite element approximations based on the uncoupled solutions.Fi- nally we present a convergence analysis and error estimates.     

Heat Flow for the Minimal Surface with Plateau Boundary Condition

The heat flow for the minimal surface under Plateau boundary condition is defined to be a parabolic variational inequality,and then the existence,uniqueness,regularity,continuous dependence on the initial data and the asymptotics are studied.It is applied as a deformation of the level sets in the critical point theory.     

关于一类新型的具边值条件的曲率流问题

本文提出了一类带有边界条件的新的曲率流问题,说明了它们的理论来源和实际背景.对Gauss曲率情形,建立了这种曲率流古典解的存在唯一性,并用一种适用于更一般曲率情形的方法,研究了这种曲率流的渐近性。     

On the Potential Flow of an Ideal Incompressible Fluid through a Porous Boundary

The potential flow of an incompressible fluid is considered.The fluid is supposed to be ideal except on the porous boundarywhere the normal velocity is proportional to the pressure. Thisleads to the Laplace equation with the square of the gradientin the boundary condition. The linearized problem (small velocities)is trivially solvable by the variational method in the usualenergy space. The nonlinearity of the boundary condition beingtoo strong for that space, the stationary problem is treatedin some Banach algebras of functions defined on the boundaryof . The existence and uniqueness of the solution are provedfor small flows or for large boundary resistances.     

第1边界条件下的n次插值曲面

提出了第1边界条件下n次插值曲面的概念,利用Lingo建模语言设计了第1边界条件下n次插值曲面的Lingo程序,并通过Excel软件得到了第1边界条件下n次插值曲面的具体表达式,运用第1边界条件下n次插值曲面,可以得到二维离散型随机变量的幂指插值形式分布律,通过一个实例给出了二维离散型总体的极大似然估计量的求法.     

On the Generalized Porous Medium Equation in Fourier-Besov Spaces

We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions.     

On a Critical Fourth Order PDE with Navier Boundary Condition

We consider a fourth order nonlinear PDE involving the critical Sobolev exponent on a bounded domain of Rⁿ, n ≥ 5 with Navier condition on the boundary. We study the lack of compactness of the problem and we provide an existence theorem through a new index formula.     

An Applicable Boundary Condition at the Moving Contact Line in Case of a Free Surface Reorientation after Step Reduction in Gravity

In this study the sudden change in the acceleration level on a free surface in a right circular cylinder is investigated numerically. The intention to describe the .uid motion encounters the difficulty modelling the moving contact‐line problem. In the numerical simulations the Navier slip boundary condition and a model for the dynamic contact angle are used. The model for the dynamic contact angle γ_d includes the dependence on the Capillary number as well as the contact angle hysteresis. We achieved very good agreement with experimental data.