Nonlinear Diffusion with Absorption

We consider the nonlinear diffusion-absorption problem in L¹() u - div a(, Du) + j (, u) f on , u = 0 on where is an arbitrary open set in ^N. Conditions for the existence of a strong solution are presented and the existence of a natural generalized solution in the general case is established. We study the dependence of the generalized solution on the absorption term j and characterize generalized solutions which are essentially bounded.     

Generalized Solutions of Nonlinear Parabolic Equations and Diffusion Processes

We reduce the construction of a weak solution of the Cauchy problem for a quasilinear parabolic equation to the construction of a solution to a stochastic problem. Namely, we construct a diffusion process that allows us to obtain a probabilistic representation of a weak (in distributional sense) solution to the Cauchy problem for a nonlinear PDE.      

Localization for a Fast Diffusion Equation with Absorption

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A Nonlinear Diffusion Problem with Localized Large Diffusion

Abstract

This paper is concerned with a nonlinear parabolic problem, with nonlinear boundary conditions, for which the diffusion coefficient becomes very large in a sub-region of the physical domain.     

Some Properties of Solutions for a Nonlinear Difusion System(II)

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A Nonlinear Diffusion System with Coupled Nonlinear Boundary Flux

This paper studies a nonlinear diffusion system with coupled nonlinear boundary flux and two kinds of inner sources （positive for the first and negative for the second）, where the four nonlinear mechanisms are described by eight nonlinear parameters. The critical exponent of the system is determined by a complete classification of the eight nonlinear parameters, which is represented via the characteristic algebraic system introduced to the problem.     

Nonlinear Diffusion Processes

We study elliptic systems of strongly nonlinear first-order differential equations in complex form on the plane. For such systems we develop the theory of Hilbert boundary value problems which is very much similar to the well-known theory for a holomorphic vector. Systems of nonlinear elliptic equations describe problems of interaction of several nonlinear stationary processes in the diffusive and convective mass and heat transport by hydrodynamic fluid flows.     

Stabilization of Nonlinear Systems with Semi-Quadratic Cost

The paper addresses the stabilization of nonlinear systems with semi-quadratic cost: quadratic with respect to controls and nonlinear for state variables. Paper presents the effective new feedback synthesis procedure. The novel feedback design procedure is based on the ideas borrowed from nonlinear optics and the theory of semi-classical asymptotics developed in quantum mechanics.     

具有扩散的Brusselator系统的Hopf分支

在齐次Neumann边界条件下,研究了Brusselator系统的Hopf分支问题.证明了当参数满足一定条件时,Brusselator常微分系统的平衡解和周期解是渐近稳定的,而相应的偏微分系统的空间齐次平衡解是不稳定的;如果适当选取参数,那么Brusselator偏微分系统出现Hopf分支.同时,利用中心流形定理证明了Hopf分支解的稳定性.最后给出一些数值模拟的例子以验证和补充理论分析结果.     

扩散过程的生存时间及其对条件扩散的应用

设τＤ是扩散过程在Ｒｄ中区域Ｄ上的生存时间．本文给出τＤ指数阶矩有限的一个充分条件．这里的区域与扩散算子都是一般的．作为应用，改进了Ｇａｏ（１９９５）关于条件扩散的主要结果．     

具非线性对流项扩散方程的源型解

研究主部为热传导算子的拟线性抛物型方程Cauchy问题:u_t=u_(xx) (u~n)_x,(x,t)∈S=R×(0,∞),u(x,0)=δ(x),x∈■在一维情形下源型解的存在性,唯一性,不存在性,解的渐近性和相似源型解等问题.在研究过程中,找到了一个n的临界值,即n_0=3.当0≤n相似文献   

具非线性对流项扩散方程的源型解

研究主部为热传导算子的拟线性抛物型方程Cauchy问题ut=uxx+(un)x, (x,t)∈S=R×(0,∞),u(x,0)=δ(x), x∈R在一维情形下源型解的存在性,唯一性,不存在性,解的渐近性和相似源型解等问题.在研究过程中,找到了一个n的临界值,即n0=3.当0≤n＜n0时,方程源型解存在且唯一;当n≥n0时,方程不存在源型解;当0≤n＜2时,方程的源型解在原点附近渐近行为恰似热传导方程的基本解;应用量纲分析技巧,证明了当且仅当n=2时,方程存在唯一相似源型解,并求出了其解析表达式.研究结果表明了这类抛物型方程对流项的存在对扩散项产生重要影响的物理事实.     

带干扰的双Poisson风险模型的破产概率

首先将[3]的双Possion风险模型推广到带干扰的一种新模型。然后运用鞅论的方法得出破产概率满足Lundberg不等式和一般公式。以及当个体所赔服从指数分布时的破产概率的具体表达式。     

Nonlinear Equations in Diffusion Theory

In this paper, we study connections between diffusion processes and some classical equations of mathematical physics and, in particular, of soliton theory. It is shown that some soliton equations correspond to one-parameter families of absolutely continuous transformations of diffusion measures and allow us to derive expressions for the logarithmic derivatives of these measures with respect to parameters. Bibliography: 8 titles.     

The Asymptotics of Nonlinear Diffusion

The asymptotic behavior of linear diffusion processes may be significantly altered by weak nonlinear effects. A method is developed for investigating such situations. Examples of both deterministic and statistical initial value problems are discussed in the one dimensional case.     

Variational Solutions to Nonlinear Diffusion Equations with Singular Diffusivity

We provide existence results for nonlinear diffusion equations with multivalued time-dependent nonlinearities related to convex continuous not coercive potentials. The results in this paper, following a variational principle, state that a generalized solution of the nonlinear equation can be retrieved as a solution of an appropriate minimization problem for a convex functional involving the potential and its conjugate. In the not coercive case, this assertion is conditioned by the validity of a relation between the solution and the nonlinearity. A sufficient condition, under which this relation is true, is given. At the end, we present a discussion on the solution existence for a particular equation describing a self-organized criticality model.     

R~n上扩散过程的代数式收敛

本文研究n维欧氏空间上的扩散过程在L2意义下的代数式收敛的情况,给出了判定代数式收敛的方法,并对两种特殊情形扩散算子进行了讨论.将所得判敛法应用于两个例子可得到精确的结果.     

流形上扩散过程的基本耦合

本文给出了光滑流形上扩散过程耦合算子的一般形式,并证明了一类耦合具有耦合的基本性质。