半平面上Euler-α方程组的边界层方程整体适定性

首先利用形式展开式得到半平面上Euler-α方程组具无滑动边界条件的边界层方程称之为Prandtl型方程.接着构造合适的解析空间,利用抽象Cauchy-Kovalevskaya定理验证该Prandtl型方程局部解的存在唯一性.最后通过求解Prandtl型方程的整体形式解,进而验证得到Prandtl型方程存在整体唯一解.     

关于一阶拟线性方程的整体解

对于非线性偏微分方程,通常局部可解性比较容易得到,而整体解问题则复杂得多.近年来,关于非线性偏微分方程的整体可解性已得到很多研究结果.比如[1]、[2]中讨论了非线性波动方程的整体可解性.[3]中讨论了某种双曲型方程组的整体可解性.[4]中讨论了某种非线性椭圆型方程的整体不可解性.也有大量工作讨论整体广义解的存在性.这些结果都是关于微分方程的初值问题或边值问题的整体可解性.但是如果我们期望得到全空间的整体解,那么如本文所得到的结果那样,微分方程本身是否存在这种整体解就是一个很值得研究的问题. 我们称方程的在全空间具有直到方程阶数的连续导数的解为全正则解.     

一类半线性椭圆型方程正整体解的存在性

本文研究了一个半线性椭圆型方程正整体解的存在性问题.利用上下解方法克服了非齐次项出现带来的困难,获得了正整体解存在的必要条件,具体地给出了在此条件下正整体解所处的领域.     

三维可压等熵Euler方程光滑解的整体存在性

研究了三维可压等熵Euler方程Cauchy问题光滑解的整体存在性.如果初值是一个常状态的小扰动并且初速度的旋度等于零,证明了三维可压等熵Euler方程Cauchy问题光滑解的整体存在性.     

带Robin边界条件的拟线性抛物方程解的整体存在性与爆破

主要研究了一类带Robin边界条件的拟线性抛物方程解的整体存在性与爆破问题,利用微分不等式技术,获得了方程的解发生爆破时的爆破时间的下界.然后给出了方程解整体存在的充分条件,最后得到了方程的解发生爆破时发生爆破时间的上界.     

一类广义非线性Euler-Poisson-Darboux方程整体解的渐近性质

W.A.Strauss等人已证明了广义非线性 Euler-Poisson-Darboux方程初边值问题整体解的存在唯一性 .本文应用一个差分不等式研究了整体解的渐近性质 .     

非均匀介质中双稳型反应对流扩散方程的整体解

本文研究了非均匀介质中双稳型反应对流扩散方程的整体解(t∈R).通过利用连接常数稳定态和不稳定态的曲面行波解,证明了整体解的存在性,该整体解表现为两列曲面行波解从无穷柱体两端相向传播、相互碰撞、并最终在有限时间内合并.进一步,在一定条件下,证明了方程的非平凡整体解是唯一的,并利用上下解方法证明了所得到的唯一整体解是Liapunov稳定的.     

高维BBM-Burgers方程解的衰减估计

本文研究了多维空间的Benjamin-Bona-Mahony-Burgers方程.在解整体存在的前提下,利用能量积分、时频分解等方法,得到此方程柯西问题解的衰减估计,并且此方程的衰减速率与热传导方程的相同.     

抽象泛函微分方程—整体解的存在性与稳定性

本文在一次近似方程的解具有指数衰减性质的条件下,采用逐步逼近方法得到了原方程整体解的存在唯一性和稳定性结果.     

混合机制对半线性热方程解爆破的抑制作用

本文考虑带有混合机制的半线性热方程,混合机制是通过加入含不可压流的对流项实现的.在没有混合机制时,方程的解在有限时间会发生爆破.在对流项合适的混合条件下,本文研究方程的大初值整体解的适定性.对于带有混合机制的经典半线性热方程,本文通过能量方法得到了整体的L~p(pd/2)估计,并且获得了经典解的整体存在性.然而,对于带有混合机制的分数阶半线性热方程,由于技术困难,通过能量方法无法得到整体的L~p (p 2)估计,这里利用非线性极值原理得到了整体的L~∞估计,并且获得了经典解的整体存在性.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.