检索结果-南通市图书馆

Gradient Estimates for a nonlinear diffusion equation on Complete Manifolds

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2015年第6期36卷 1011-1018页

作者： Jiaxian WU Qihua RUAN Yihu YANG School of Mathematics and Statistics Nanjing University of Information Science & Technology Department of Mathematics Putian University Department of Mathematics Shanghai Jiao Tong University

This paper deals with the gradient estimates of the Hamilton type for the positive solutions to the following nonlinear diffusion equation：on a complete noncompact Riemannian manifold with a Bakry-Emery Ricci curvature bounded below by -K （K 〉 0）, where φ is a C2 function, a（x） and b（x） are C1 functions with certain conditions.

关键词： Gradient estimate Bakry-Emery Ricci curvature nonlinear diffusion equation 58J35

Gradient Estimates for a nonlinear diffusion equation on Complete Manifolds

在线全文

学校读者我要写书评

暂无评论

Journal of Partial Differential equations 2010年第1期23卷 68-79页

作者： WU Jiayong Department of Mathematics East China Normal University Shanghai 200241 China.

Let （M,g） be a complete non-compact Riemannian manifold with the m- dimensional Bakry-Emery Ricci curvature bounded below by a non-positive constant. In this paper, we give a localized Hamilton-type gradient estimate for the positive smooth bounded solutions to the following nonlinear diffusion equation ut = △u - △↓ φ· △ ↓u - aulogu- bu,where φ is a C^2 function, and a ≠ 0 and b are two real constants. This work generalizes the results of Souplet and Zhang （Bull. London Math. Soc., 38 （2006）, pp. 1045-1053） and Wu （Preprint, 2008）.

关键词： Local gradient estimate nonlinear diffusion equation Bakry-Emery Ricci curvature.

Functional Separable Solutions to nonlinear diffusion equations by Group Foliation Method

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2007年第2期47卷 193-199页

作者： HU Jia-Yi QU Chang-Zheng YIN Hui Center for nonlinear Studies Northwest University Xi＇an 710069 China Department of Mathematics Northwest University Xi＇an 710069 China Department of Mathematics South-Central University of Nationalities Wuhan 430074 China Wuhan Institute of Physics and Mathematics the Chinese Academy of Sciences Wuhan 430071 China

We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.

关键词： group foliation method functional separation of variable nonlinear diffusion equation symmetry group

Conditional Symmetry Groups of nonlinear diffusion equations with x-Dependent Convection and Absorption

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2004年第2期41卷 231-234页

作者： QUChang-Zheng ZHANGShun-Li DepartmentofMathematics NorthwestUniversityXi＇an710069China

The generalized conditional symmetry and sign-invariant approaches are developed to study the nonlinear diffusion equations with x-dependent convection and source terms. We obtain conditions under which the equations admit the second-order generalized conditional symmetries and the first-order sign-invariants on the solutions. Several types of different generalized conditional symmetries and first-order sign-invariants for the equations with diffusion of power law are obtained. Exact solutions to the resulting equations are constructed.

关键词： symmetry group sign-invariant nonlinear diffusion equation exact solution

Potential Symmetries to a System of Three-Component nonlinear diffusion equations

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2006年第2期45卷 193-198页

作者： XUE Chun-Rong QU Chang-Zheng Center for nonlinear Studies Northwest University Xi＇an 710069 China Department of Mathematics Northwest University Xi＇an 710069 China

A system of nonlinear diffusion equations with three components is studied via the potential symmetry method. It is shown that the system admits the potential symmetries for certain diffusion terms. The invariant solu... 详细信息

关键词： Lie point symmetry potential symmetry nonlinear diffusion equation group-invariant solutions

Ma’s Variation of Parameters Method for Fisher’s equations

在线全文

学校读者我要写书评

暂无评论

Advances in Applied Mathematics and Mechanics 2010年第3期2卷 379-388页

作者： Syed Tauseef Mohyud-Din Ahmet Yıldırım HITEC University Taxila Cantt Pakistan Ege University Department of Mathematics35100 Bornova-IzmirTurkey

In this paper,we apply Ma’s variation of parameters method(VPM)for solving Fisher’s *** suggested algorithm proved to be very efficient and finds the solution without any discretization,linearization,perturbation or... 详细信息

关键词： Variation of parameters method variational iteration method nonlinear problems Fisher’s equation nonlinear diffusion equation error estimates

Anomalous Dimension in the Solution of the Modified Porous Medium equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2002年第6期37卷 741-744页

作者： TUTao CHENGGeng 等 LaboratoryofQuantumCommunicationandQuantumComputation UniversityofScienceandTechnologyofChinaHefei230026China DepartmentofAstronomyandAppliedPhysics UniversityofScienceandTech

A new method - perturbative summation to infinite order is presented to obtain the anomalous dimension in the solution of the modified porous medium equation. The result is the same as that in the renormalization group (RG) approach. It gives us an insight into the anomalous exponent in the asymptotic solution of the modified porous medium equation in the RG approach. Based on this discussion, we can see that the anomalous dimension appears naturally in the problem and the nonlinearity reflects the anomalous long-time behavior of the system.

关键词： renormalization group asymptotic analysis nonlinear diffusion equation

Hydrodynamic Limit for Exclusion Processes

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Mathematics and Statistics 2018年第4期6卷 417-480页

作者： Tadahisa Funaki Department of Mathematics School of Fundamental Science and EngineeringWaseda University3-4-1 OkuboShinjuku-kuTokyo 169-8555Japan

The exclusion process,sometimes called Kawasaki dynamics or lattice gas model,describes a system of particles moving on a discrete square lattice with an interaction governed by the exclusion rule under which at most one particle can occupy each *** mostly discuss the symmetric and reversible *** weakly asymmetric case recently attracts attention related to KPZ equation;*** and Giacomin(Commun Math Phys 183:571–607,1995)for a simple exclusion case and Gonçalves and Jara(Arch Ration Mech Anal 212:597–644,2014)for an exclusion process with speed change,see also Gonçalves et al.(Ann Probab 43:286–338,2015),Gubinelli and Perkowski(J Am Math Soc 31:427–471,2018).In Sect.1,as a warm-up,we consider a simple exclusion process and discuss its hydrodynamic limit and the corresponding fluctuation limit in a proper space–time *** this model,one can derive a linear heat equation and a stochastic partial differential equation(SPDE)in the limit,*** 2 is devoted to the entropy method originally invented by Guo et al.(Commun Math Phys 118:31–59,1988).We consider the exclusion process with speed change,in which the jump rate of a particle depends on the configuration nearby the *** gives a non-trivial interaction among *** study only the case that the jump rate satisfies the so-called gradient *** hydrodynamic limit,which leads to a nonlinear diffusion equation,follows from the local ergodicity or the local equilibrium of the system,and this is shown by establishing one-block and twoblock *** also discuss the fluctuation limit which follows by showing the so-called Boltzmann–Gibbs *** 3 explains the relative entropy method originally due to Yau(Lett Math Phys 22:63–80,1991).This is a variant of GPV method and gives another proof for the hydrodynamic *** difference between these two methods is as *** N^(d)be the volume of the domain on which the system is defined(typically,d-dim

关键词： Exclusion process Kawasaki dynamics Hydrodynamic limit Scaling limit Relative entropy nonlinear diffusion equation

Localization for a Fast diffusion equation with Absorption

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Mathematical Research 1999年第2期 27-32页

作者： Yuan Hongjun (Institute of Mathematics, Jilin University, Changchun, 130012)

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｓｉｄｅｒｔｈｅｆａｓｔｄｉｆｕｓｉｏｎｅｑｕａｔｉｏｎｗｉｔｈａｂｓｏｒｐｔｉｏｎｕｔ＝Δｕｍ－ｕｐ（１）ｉｎＱ＝Ｒｎ×（０，＋∞）ｗｉｔｈｔｈｅｉｎｉ... 详细信息

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｓｉｄｅｒｔｈｅｆａｓｔｄｉｆｕｓｉｏｎｅｑｕａｔｉｏｎｗｉｔｈａｂｓｏｒｐｔｉｏｎｕｔ＝Δｕｍ－ｕｐ（１）ｉｎＱ＝Ｒｎ×（０，＋∞）ｗｉｔｈｔｈｅｉｎｉｔｉａｌｃｏｎｄｉｔｉｏｎｕ（ｘ，...

关键词： Localization nonlinear diffusion equation Fast diffusion equation