The Asymptotic Property of Solutions to a Class of Integrodifferential Equations

The asymptotic property of solutions to a class of integrodifferential systems containing a small parameter singularly is studied.     

SomePropertiesofSolutionsforaNonlinearDifusionSystem（I）

ＳｏｍｅＰｒｏｐｅｒｔｉｅｓｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＮｏｎｌｉｎｅａｒＤｉｆｕｓｉｏｎＳｙｓｔｅｍ（Ｉ）＊）ＷｕＺｈｕｏｑｕｎ（伍卓群）ａｎｄＹｉｎＪｉｎｇｘｕｅ（尹景学）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒ...     

一类拟线性超抛物方程的整体解

<正> §1超抛物方程最早是由从概率论的问题中提出的.这种方程在附面层理论和布朗运动的理论中也要遇到.对于这种特殊的退缩抛物方程,有关一般退缩抛物方程的结果当然都可以应用;但超抛物方程的特殊性却同时要求(也有可能)对它作进一步的研究.在这方面,早在六十年代前期就有过不少工作(例如[1],[2]).至于拟线     

SOME GENERAL RESULTS ON THE FIRST BOUNDARY VALUE PROBLEM FOR QUASILINEAR DEGENERATE PARABOLICE QUATIONS

In this paper,the authors investigate the first boundary value problem for equations ofthe formwithAn existence theorem of solution in BV_(1,1/2)(Q_T)is proved.The principal condition is thatthere exists δ>0 such that for any(x,t)∈Q_T,|u|≤Ma~(ij)(u,x,t)ξ_iξ_j-δ(a_(x_θ)~(ij)(u,x,t)ξ_i)~2≥0.a, ~=1     

Periodic Solutions of Porous Medium Equations with Weakly Nonlinear Sources

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＴｈｉｓｐａｐｅｒｉｓｃｏｎｃｅｒｎｅｄｗｉｔｈｔｈｅｔｉｍｅｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｓｏｆｔｈｅｐｏｒｏｕｓｍｅｄｉｕｍｅｑｕａｔｉｏｎｓｗｉｔｈｗｅａｋｌｙｎｏｎｌｉｎｅａｒｓｏｕｒｃｅｓａｎｄｗｉｔｈｔｈｅＤｉｒｉｃｈｌｅｔｂｏｕｎｄａｒｙｖａｌｕｅｃｏｎｄｉｔｉｏｎ ,ｎａｍｅｌｙ ,ｔｈｅｐｒｏｂｌｅｍ ｕ ｔ =Δ(｜ｕ｜ｍ- 1ｕ) +Ｂ(ｘ ,ｔ,ｕ) +ｆ(ｘ ,ｔ)　ｉｎΩ×Ｒ ,(1 .1 )ｕ(ｘ ,ｔ) =0　ｏｎ Ω×Ｒ , (1 .2 )ｕ(ｘ ,ｔ+ω) =ｕ(ｘ ,ｔ)　ｉｎ Ω×Ｒ ,…     

Time periodic solutions of a class of degenerate parabolic equations

1.IntroductionManypapershavebeendevotedtotheexistenceoftimeperiodicsolutionsforsemilinearparabolicequations,see[1--8].Atthesametime,thestudyofquasilinearperiodic-parabolicequationsalsoattractedmanyauthors,seealso[9--141.Inparticular,recentlyHess,PozioandTesei[13]usedthemonotonicitymethodstodealwiththeequationsonot=aam a(x,t)u,wherem>1andaisafunctionperiodicint,andMizoguchi[lllappliedtheLeray-Schauderdegreetheorytoinvestigatetheequationswithsuperlinearforcingtermwherem>1,hisapositiveperiodicf…     

Existence and Nonuniqueness of Weak Solutions of the Initial-Boundary Value Problem for ut=u^σ div（｜△↓u｜^（p-2）△↓u）

In this paper, we study the existence and nonuniqueness of weak solutions of the initial and boundary value problem for ut =u^σ div(|△↓u|^(p-2)△↓u) with σ≥1. Localization property of weak solutions is also discussed.     

Uniqueness of BV Entropy Solutions for Higher Dimensional Quasilinear Parabolic Equations with Arbitrary Degeneracy

We are concerned with the uniqueness of solutions of the Cauchy problemand a(s),b(s) are appropriately smooth.Since a(s) is allowed to have zero points, we call them points of degeneracy of (1), the equation (1) does not admit classical solutions in general. The solutions of (1) even might be discontinuous, whenever the set E = {s : a(s) = 0} includes interior points.Equations with degeneracy arise from a wide variety of diffusive processes in nature     

常微分方程的奇摄动理论

如所周知,含小参数的微分方程在应用上是屡见不鲜的。鉴于参数小,人们往往近似地去考虑参数为零时的方程,即所谓“退化”方程。自然必须研究,“退化”方程在何种程度上从定量和定性方面反映了原方程的状况。按照方程含参数的方式,可以分成本质上不同的两种情形,即所谓寻常情形和奇异情形。为了考察作为原方程的第一近似的“退化”方程的近似程度,即由小参数所表征的摄