数学季刊

楼与群I

黎景辉, 梁志斌

2020, 35(1): 1-28. doi:10.13371/j.cnki.chin.q.j.m.2020.01.001

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This is a pedagogical introduction to the theory of buildings of Jacques Tits and to some applications of this theory.This paper has 4 parts.In the first part we discuss incidence geometry,Coxeter systems and give two definitions of buildings.We study in the second part the spherical and affine buildings of Chevalley groups.In the third part we deal with Bruhat-Tits theory of reductive groups over local fields.Finally we discuss the construction of the p-adic flag manifolds.

一类带非线性边界条件的非经典扩散方程解的爆破

张芳红, 白莉红

2020, 35(1): 29-36. doi:10.13371/j.cnki.chin.q.j.m.2020.01.002

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In this article,under suitable conditions on the internal term f（·） and the boundary nonlinear term g（·）,we prove blow-up results for a class of nonclassical diffusion equations with nonlinear boundary condition.

一类不确定薛定谔基尔霍夫方程解的存在性和集中性

陈玉松, 常荷洁

2020, 35(1): 37-45. doi:10.13371/j.cnki.chin.q.j.m.2020.01.003

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This paper is concerned with the nonlinear Schrodinger-Kirchhoff system $-(a+b \int _{R^{3}}|\nabla u|^{2} dx) \triangle u+ \lambda V(x)u=f(x,u)$ in R³, where constants a > 0,b ≥ 0 and λ > 0 is a parameter. We require that V (χ) ∈ C(R³) and has a potential well V ^-1(0). Combining this with other suitable assumptions on K and ƒ, the existence of nontrivisd solutions is obtained via vaxiational methods. Furthermore, the concentration behavior of the nontrivial solution is also explored on the set V ^-1(0) as λ → + ∞ as well. It is worth noting that the (PS )-condition can not be directly got as done in the literature, which makes the problem more complicated. To overcome this difficulty, we adopt different method.

一类不确定薛定谔基尔霍夫方程解的存在性和集中性

刘讲军, 曲桢, 胡钢

2020, 35(1): 46-55. doi:10.13371/j.cnki.chin.q.j.m.2020.01.004

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In this paper, we investigate the regularity criterion via the pressure of weak solutions to the micropolar fluid equations in three dimensions. We obtain that for 0 < a < 1 if $p \epsilon L^{\frac{2}{\alpha}} (0,T, \dot{B}_{\infty, \infty}^{\alpha})$, then the weak solution (υ,ω) is regular on (0, T].

带有二项式系数的广义Fibonacci和Lucas数一个结果的拓广

薛琳, 张之正

2020, 35(1): 56-62. doi:10.13371/j.cnki.chin.q.j.m.2020.01.005

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The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients. These results generalize the identities by Gulec, Taskaxa and Uslu in Appl. Math. Lett. 23(2010) 68-72 and Appl. Math. Comput. 220(2013) 482-486.

b₂-度量空间中一对广义循环收缩映射的公共不动点定理

王亚敏, 赛朋飞

2020, 35(1): 63-76. doi:10.13371/j.cnki.chin.q.j.m.2020.01.006

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In this paper, we introduce the notion of generalized cyclic contraction pairs in b₂-metric spaces and establish some fixed point theorems for such pairs. Then，we give an example to illustrate our results.

具有一般非线性耦合项的抛物型方程组的爆破时间估计

胡彩华, 李锋杰, 王千喜

2020, 35(1): 77-92. doi:10.13371/j.cnki.chin.q.j.m.2020.01.007

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This paper deals with some parabolic equations, where the reaction and the boundary flux are taken of some general forms. We study the explicit blow-up time estimates according to the different coupled relationship, including the lower and upper bounds of blow-up time for every dimension of space domains. As examples, the results could be used to so many completely coupled models.

带有非线性项不可压Navier-Stokes方程整体性吸引子的存在性

郑治波, 张利萍, 郝晓红, 刘国旗, 孙江洁

2020, 35(1): 93-110. doi:10.13371/j.cnki.chin.q.j.m.2020.01.008

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This paper is concerned with the Navier-stokes equations with nonlinear perturbation in R² which studies the existence of solution, and gets the existence of the attractors. Finally, we discuss with limit-behavior of the Navier-stokes equation4 with nonlinear perturbation, as a → 0.

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