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1.
蒋良军 《数学季刊》2015,(2):244-252
In this paper,we deal with the blow-up property of the solution to the diffusion equation u_t = △u + a(x)f(u) ∫_Ωh(u)dx,x∈Ω,t0 subject to the null Dirichlet boundary condition.We will show that under certain conditions,the solution blows up in finite time and prove that the set of all blow-up points is the whole region.Especially,in case of f(s) = s~p,h(s) = s~q,0 ≤ p≤1,p + q 1,we obtain the asymptotic behavior of the blow up solution.  相似文献   

2.
Let q be a prime power. By PL(Fq) the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △(3, 3, k) = (u, v: u^3 = v^3 = (uv)^k = 1〉on PL(Fq), where q ≡ ±1(modk). Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △(3, 3, k) on PL(Fq). The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by (u^-v^-)^k. In this way, they get △(3, 3, k) as permutation groups on PL(Fq).  相似文献   

3.
In this paper,we consider the following system of integral equations on upper half space {u(x) = ∫Rn + (1/|x-y|n-α-1/|-y|n-α) λ1up1(y) + μ1vp2(y) + β1up3(y)vp4(y) dy;v(x) = ∫Rn + (1/|x-y|n-α-1/|-y|n-α)(λ2uq1(y) + μ2vq2(y) + β2uq3(y)vq4(y) dy,where Rn + = {x =(x1,x2,...,xn) ∈ Rn|xn 0}, =(x1,x2,...,xn-1,-xn) is the reflection of the point x about the hyperplane xn= 0,0 α n,λi,μi,βi≥ 0(i = 1,2) are constants,pi≥ 0 and qi≥ 0(i = 1,2,3,4).We prove the nonexistence of positive solutions to the above system with critical and subcritical exponents via moving sphere method.  相似文献   

4.
Let BR be the ball centered at the origin with radius R in RN ( N ≥2). In this paper we study the existence of solution for the following elliptic systemu -△u+λu=p/(p + q)κ(| x |)) u(p-1)vq1,x ∈BR1,-△u+λu=p/(p + q)κ(| x |)) upv(q-1)1,x ∈BR1,u > 01,v > 01,x ∈ BR1,(u)/(v)=01,(v)/(v)=01,x ∈BRwhereλ > 0 , μ > 0 p ≥ 2, q ≥ 2,ν is the unit outward normal at the boundary BR . Under certainassumptions on κ ( | x | ), using variational methods, we prove the existence of a positive and radially increasing solution for this problem without growth conditions on the nonlinearity.  相似文献   

5.
We consider the system of four linear matrix equations A1X = C1, XB2=C2, A3XB3=C3 and A4XB4 = C4 over h, an arbitrary von Neumann regular ring with identity. A necessary and sufficient condition for the existence and the expression of the general solution to the system are derived. As applications, necessary and sufficient conditions are given for the system of matrix equations A1X = C1 and A3X=C3 to have a bisymmetric solution, the system of matrix equations A1X = C1 and A3XB3 = C3 to have a perselfconjugate solution over h with an involution and char h≠2, respectively. The representations of such solutions are also presented. Moreover, some auxiliary resultson other systems over h are obtained. The previous known results on some systems of matrix equations are special cases of the new results.  相似文献   

6.
Let G be an outerplanar graph with maximum degree △. Let χ(G^2) and A(G) denote the chromatic number of the square and the L(2, 1)-labelling number of G, respectively. In this paper we prove the following results: (1) χ(G^2) = 7 if △= 6; (2) λ(G) ≤ △ +5 if △ ≥ 4, and ),(G)≤ 7 if △ = 3; and (3) there is an outerplanar graph G with △ = 4 such that )λ(G) = 7. These improve some known results on the distance two labelling of outerplanar graphs.  相似文献   

7.
Consider I pairs of independent binomial variates x0i and x1i with corresponding parameters P0i and p1i and sample sizes n0i and n1i for i=1, …,I. Let △i = P1i-P0i be the difference of the two binomial parameters, where △i's are to be of interest and P0i's are nuisance parameters. The null hypothesis of homogeneity on the risk difference can be written as  相似文献   

8.
Very recently, Yu, Le and Zhou introduced the so called △B1^* and △B2^* conditions, which are generalizations of the monotone condition. By applying these two new conditions, the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric series. In fact, the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series, where coefficients may have different signs.  相似文献   

9.
CLASSICAL SOLUTION OF QUASI-STATIONARY STEFAN PROBLEM   总被引:2,自引:1,他引:1  
This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv (?)u/(?)u=0 on the free boundary.Under the natural conditions the existence of classical solution locally in time is proved bymaking use of the property of Frechet derivative operator and fixed point theorem. For thesake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can bedealt with in a similar way with more complicated calculation.  相似文献   

10.
Abstract In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions: {ut-a(u, v)△u=g(u, v), vt-b(u, v)△v=h(u, v), δu/δη=d(u, v), δu/δη=f(u, v).Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques.  相似文献   

11.
In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank. Our formula is different from that of Siegel’s. As an application, we get a polynomial representation of ζK(-1): ζK(-1) = 1/45(26n3 -41n± 9),n = ±2(mod 5), where K = Q(√5q), prime q = 4n2 + 1, and the class number of quadratic number field K2 = Q(vq) is 1.  相似文献   

12.
We obtain new unimprovable Kolmogorov-type inequalities for differentiable periodic functions. In particular, we prove that, for r = 2, k = 1 or r = 3, k = 1, 2 and arbitrary q, p [1, ], the following unimprovable inequality holds for functions :
where and r is the perfect Euler spline of order r.  相似文献   

13.
LetS(q, d) be the maximal numberv such that, for every general position linear maph: Δ(q?1)(d+1)R d, there exist at leastv different collections {Δ t1, ..., Δ t q} of disjoint faces of Δ(q?1)(d+1) with the property thatf t1) ∩ ... ∩f t q) ≠ Ø. Sierksma's conjecture is thatS(q, d)=((q?1)!) d . The following lower bound (Theorem 1) is proved assuming thatq is a prime number: $$S(q,d) \geqslant \frac{1}{{(q - 1)!}}\left( {\frac{q}{2}} \right)^{{{((q - 1)(d + 1))} \mathord{\left/ {\vphantom {{((q - 1)(d + 1))} 2}} \right. \kern-\nulldelimiterspace} 2}} .$$ Using the same technique we obtain (Theorem 2) a lower bound for the number of different splittings of a “generic” necklace.  相似文献   

14.
本文讨论带Dirichlet边界条件的反应扩散方程组ut(x,t)=△u(x,t)+uα(x,t).up(0,t),vt(x,t)=△v(x,t)+uβ(x,t)vq(0,t),研究了该问题正解的爆破性质并给出爆破集及其爆破速率.  相似文献   

15.
Summary We construct germs of holomorphic diffeomorphisms of (C, 0),f(z) =e 2i z +O(z 2), R–Q, non linearizable and having an uncountable centralizer, that is an uncountable number of symmetries. This gives a positive answer to a question of M.R. Herman. We construct such examples having no periodic orbit (except 0), and also with a sequence of periodic orbits tending to 0 (distinct from 0). Moreover the examples constructed have an infinite number of finite order symmetries, and the dynamics is quite explicit. We also construct non linearizable analytic diffeomorphisms of the circle having an irrational rotation number and uncountable centralizer with similar properties.
Résumé On construit des germes de difféomorphismes holomorphes de (C, 0),f(z) =e 2i z +O(z 2), R–Q, non linéarisables et ayant un centralisateur non dénombrable, i.e. un nombre non dénombrable de symétries. Ceci répond positivement à une question de M.R. Herman. On construit de tels exemples sans orbite périodique (sauf 0) et d'autres ayant une suite d'orbites périodiques tendant vers 0 (et différentes de 0). De plus, ces exemples ont un nombre infini de symétries d'ordre fini, et leur dynamique est assez explicite. On construit également des difféomorphismes analytiques du cercle non linéarisables, de nombre de rotation irrationel ayant un centralisateur non dénombrable et des propriétés analogues aux précédentes.
  相似文献   

16.
Summary Given an integern 1, and the orthogonal polynomials n (·; d) of degreen relative to some positive measured, the polynomial system induced by n is the system of orthogonal polynomials corresponding to the modified measure . Our interest here is in the problem of determining the coefficients in the three-term recurrence relation for the polynomials from the recursion coefficients of the orthogonal polynomials belonging to the measured. A stable computational algorithm is proposed, which uses a sequence ofQR steps with shifts. For all four Chebyshev measuresd, the desired coefficients can be obtained analytically in closed form. For Chebyshev measures of the first two kinds this was shown by Al-Salam, Allaway and Askey, who used sieved orthogonal polynomials, and by Van Assche and Magnus via polynomial transformations. Here, analogous results are obtained by elementary methods for Chebyshev measures of the third and fourth kinds. (The same methods are also applicable to the other two Chebyshev measures.) Interlacing properties involving the zeros of n and those of are studied for Gegenbauer measures, as well as the orthogonality—or lack thereof—of the polynomial sequence .Work supported in part by the National Science Foundation under grant DMS-9023403.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth.  相似文献   

17.
Certain search algorithms produce a sequence of decreasing regions converging to a pointx *. After renormalizing to a standard region at each iteration, the renormalized location ofx *, sayx x, may obey a dynamic process. In this case, simple ergodic theory might be used to compute asymptotic rates. The family of second-order line search algorithms which contains the Golden Section (GS) method have this property. The paper exhibits several alternatives to GS which have better almost sure ergodic rates of convergence for symmetric functions despite the fact that GS is asymptotically minimax. The discussion in the last section includes weakening of the symmetry conditions and announces a backtracking bifurcation algorithm with optimum asymptotic rate.  相似文献   

18.
We give several characterizations of those sequences of holomorphic self-maps {φ n } n≥1 of the unit disk for which there exists a function F in the unit ball of H such that the orbit {F∘φ n :n∈ℕ} is locally uniformly dense in . Such a function F is said to be a -universal function. One of our conditions is stated in terms of the hyperbolic derivatives of the functions φ n . As a consequence we will see that if φ n is the nth iterate of a map φ of into , then {φ n } n≥1 admits a -universal function if and only if φ is a parabolic or hyperbolic automorphism of . We show that whenever there exists a -universal function, then this function can be chosen to be a Blaschke product. Further, if there is a -universal function, we show that there exist uniformly closed subspaces consisting entirely of universal functions.  相似文献   

19.
关于Fujita型反应扩散方程组的Cauchy问题   总被引:5,自引:1,他引:5  
张凯军  王亮涛 《数学学报》1997,40(5):717-732
本文研究Fujita型反应扩散方程组ut-Δu=α1|u|q1-1u+β1|v|p1-1v,(x∈RN,t>0),vt-Δv=α2|u|q2-1u+β2|v|p2-1v,u(x,0)=u0(x)0,v(x,0)=v0(x)0,(x∈RN)Lp解的整体存在性和有限时间Blow up问题.这里qi>1,pi>1(i=1,2),α10,α2>0,β1>0,β20,1p+∞.  相似文献   

20.
Summary The success of the cyclic Richardson iteration depends on the proper ordering of the acceleration parameters. We give a rigorous error analysis to show that, with the proper ordering, the relative error in the iterative method, when properly terminated, is not larger than the error incurred in stable direct methods such as Cholesky factorization. For both the computed approximation tou=L –1f satisfies cond (L)u2–t and this bound is attainable. We also show that the residual norm is bounded by L cond . This bound is attainable for a small cycle lengthN. Our analysis suggests that for a larger cycle lengthN the residuals are bounded by . We construct a theoretical example in which this bound is attainable. However we observed in all numerical tests that ultimately the residual norms were of order . We explain why in practice even the factor is never encountered. Therefore the residual stopping criterion for the Richardson iteration appears to be very reliable and the method itself appears to be stable.The author gratefully acknowledges partial support from ONR Contract N00014-85-K-0180On leave from the University of Krakow, Poland, during the spring semester 1989  相似文献   

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