一类具有非线性阻尼和源项的Petrovsky方程整体解的存在性与渐近性

研究了一类具有非线性阻尼和源项的Petrovsky方程u_(tt) △~2u au_t|u_t|~(m-2)= bu|u|~(p-2)的初边值问题.在对m,p的大小关系不加任何限制的情况下,利用稳定集证明了整体解的存在性,并且得到了整体解的渐近性质.     

一类非线性四阶波动方程的位势井方法

该文讨论非线性波动方程u_{tt}+u_{xxxx}=σ(u_x)_x+f(x,t)的初边值问题.证明了整体弱解的存在性,还证明了整体广义解的存在唯一性和整体古典解的存在唯一性.     

具阻尼项的Boussinesq型方程的长时间行为

该文研究具阻尼项的Boussinesq型方程u_(tt)-△u+△~2u-△u_t-△g(u)=f(x)初边值问题的解的长时间行为.利用半群分解的方法证明了上述问题对应的无穷维动力系统在能量相空间E=V_2×H中整体吸引子的存在性和吸引子Hausdorff维数的有限性,其中对非线性项g(u)的抽象条件加以验证并给出具体实例.     

具有阻尼的半线性波动方程解的衰减估计

研究具有阻尼的半线性波动方程的初边值问题u_(tt)-△u+βu_t=|u|~(p-1)u,x∈Ω,t>0u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈Ωu|_((?)Ω)=0,t≥0其中γ为正常数,Ω■R~n为有界域,当n≥3时,1相似文献   

一类具有非线性阻尼和源项的Petrovsky方程初边值问题解的爆破

研究一类具有非线性阻尼和源项的Petrovsky方程u_(tt)+△~2u+au_t|u_t|~(m-2)=bu|u|~(p-2)的初边值问题解的爆破,利用不稳定集证明了当m相似文献   

四阶具强阻尼非线性波动方程解的整体存在性与不存在性

研究四阶具强阻尼非线性波动方程utt-△u+△2u-α△ut=f(u)的初边值问题.利用位势井方法,得到了问题整体解存在性与不存在性的最佳条件(门槛结果).     

非线性Klein-Gordon方程柯西问题解的整体存在性与Blow-up

研究非线性Klein-Gordon方程的柯西问题u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0;u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n.通过引进一族位势井,得到了解的整体存在性与不存在的门槛结果.     

四阶具强阻尼非线性波动方程解的整体存在性与不存在性

研究四阶具强阻尼非线性波动方程utt-△u+△~2u-α△ut=f(u)的初边值问题.利用位势井方法,得到了问题整体解存在性与不存在性的最佳条件(门槛结果).     

一类高阶非线性波动型方程整体解的存在性和指数衰减性

研究了一类带有阻尼和源项的高阶非线性波动方程u_(tt)+A+u_t+aAu_t=b|u|~(q-1)u的初边值问题,这里A=(-△)m,m≥1是一个自然数,a≥0,b 0和q1是实数通过构造稳定集证明了这个问题整体解的存在,并应用乘子方法建立了整体解的指数衰减估计同时,在初始能量非负和a=0的条件下,得到了解在有限时间内发生爆破.     

一类非线性非自治可伸缩板方程的一致吸引子

讨论了一类带有初值条件和固定边界条件的非线性非自治可伸缩板方程u_(tt)+△~2u+αu-△u_(tt)-M(||▽u||~2)△u-γ△u_t+f(u)=σ(x,t)证明了该系统的整体适定性.进一步研究了该系统的长时间动力学,利用建立整体弱解所生成的半过程一致渐近紧性,得到了有界区域Ω■R~n(n≥1)或无界开集中一致吸引子的存在性.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.