共查询到20条相似文献,搜索用时 15 毫秒
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V. V. Lychagin 《Journal of Mathematical Sciences》1990,51(6):2735-2757
The article is devoted to singularities of integral manifolds which realize solutions of nonlinear partial differential equations and to the algebraic geometric and topological questions related to them.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 20, pp. 207–247, 1988. 相似文献
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A. V. Pokrovskii 《Mathematical Notes》2005,77(3-4):539-545
Suppose that P(x, D) is a linear differential operator of order m > 0 with smooth coefficients whose derivatives up to order m are continuous functions in the domain G n (n 1), 1 < p > , s > 0, and q=p/(p – 1). In this paper, we show that if n, m, p, and s satisfy the two-sided bound 0 n – q(m – s)< n, then for a weak solution of the equation P(x, D)u=0 from the Sharpley-DeVore class C
p
s
(G)loc, any closed set in G is removable if its Hausdorff measure of order n – q(m – s) is finite. This result strengthens the well-known result of Harvey and Polking on removable singularities of weak solutions to the equation P(x, D)u=0 from the Sobolev classes and extends it to the case of noninteger orders of smoothness.Translated from Matematicheskie Zametki, vol. 77, no. 4, 2005, pp. 584–591.Original Russian Text Copyright © 2005 by A. V. Pokrovskii.This revised version was published online in April 2005 with a corrected issue number. 相似文献
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On periodic solutions of second-order differential equations with attractive-repulsive singularities
Sufficient conditions for the existence of a solution to the problem
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Lars Hörmander 《Israel Journal of Mathematics》1972,13(1-2):82-105
LetP be a differential operator with constant coefficients in ℝ
n
. Ifu is a distribution, the singular support ofu is the complement of the largest set whereu ∈C
∞. Necessary and sufficient conditinos are obtained for a closed convex set Γ to be equal to the singular support ofu for someu withPu ∈C
∞ or, equivalently, for Γ to contain the singular support ofu for someu withPu ∈C
∞ butu ∉C
∞. Related local uniqueness theorems analogous to the Holmgren theorem with supports replaced by singular supports are also
given, as well as applications concerningP-convexity with respect to singular supports. 相似文献
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Numerical Algorithms - This study is concerned with numerical approximations of time-fractional stochastic heat-type equations driven by multiplicative noise, which can be used to model the... 相似文献
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In this paper, we introduce an extension of multiple set split variational inequality problem (Censor et al. Numer. Algor. 59, 301–323 2012) to multiple set split equilibrium problem (MSSEP) and propose two new parallel extragradient algorithms for solving MSSEP when the equilibrium bifunctions are Lipschitz-type continuous and pseudo-monotone with respect to their solution sets. By using extragradient method combining with cutting techniques, we obtain algorithms for these problems without using any product space. Under certain conditions on parameters, the iteration sequences generated by the proposed algorithms are proved to be weakly and strongly convergent to a solution of MSSEP. An application to multiple set split variational inequality problems and a numerical example and preliminary computational results are also provided. 相似文献
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耿晓晶 《纯粹数学与应用数学》2013,(6):646-653
由于多维马尔科夫转制随机微分方程不存在解析解,利用Euler—Maruyama方法给出多维马尔科夫转制随机微分方程的渐进数值解,并证明了此数值解收敛到方程的解析解.将单一马尔科夫转制随机微分方程的数值解问题延伸到多维马尔科夫转制情形,增强了马尔科夫转制随机微分方程的适用性. 相似文献
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A. V. Pokrovskii 《Journal of Mathematical Sciences》2009,160(1):61-83
This paper is an overview of results devoted to metric conditions for removability of closed sets for solutions of homogeneous
partial differential equations in various function classes. The author considers equations with a quasi-homogeneous semi-elliptic
operator and with constant coefficients, linear second-order uniformly elliptic equations in the divergent form with real
bounded measurable coefficients, quasilinear equations with the p-Laplacian, and the minimal surface equation. A number of results is published for the first time.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 57, Suzdal
Conference–2006, Part 3, 2008. 相似文献
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A. V. Pokrovskii 《Differential Equations》2009,45(2):209-216
Let P(D) be a quasihomogeneous semi-elliptic linear differential operator with constant coefficients in ? n . We prove a metric criterion for the removability of singular sets of solutions of the equation P(D)f = 0 in function classes defined by solutions of this equation with the use of local approximations in mean. 相似文献
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We prove the existence of periodic solutions for the equation
(1) 相似文献
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Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations 总被引:3,自引:0,他引:3
The characteristic equation of a system of delay differential equations (DDEs) is a nonlinear equation with infinitely many
zeros. The stability of a steady state solution of such a DDE system is determined by the number of zeros of this equation
with positive real part. We present a numerical algorithm to compute the rightmost, i.e., stability determining, zeros of
the characteristic equation. The algorithm is based on the application of subspace iteration on the time integration operator
of the system or its variational equations. The computed zeros provide insight into the system’s behaviour, can be used for
robust bifurcation detection and for efficient indirect calculation of bifurcation points.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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In this paper, we study the numerical solution of fuzzy differential equations by using hybrid Euler method and hybrid predictor-corrector method. These methods are used to increase the accuracy and the computing speed. Also examples are presented to illustrate the computational aspects of the above methods. 相似文献