The Cauchy Problem for a Class of Semilinear Wave Equations with Piecewise Constants Data

ＴｈｅＣａｕｃｈｙＰｒｏｂｌｅｍｆｏｒａＣｌａｓｓｏｆＳｅｍｉｌｉｎｅａｒＷａｖｅＥｑｕａｔｉｏｎｓｗｉｔｈＰｉｅｃｅｗｉｓｅＣｏｎｓｔａｎｔｓＤａｔａＺｈａｎｇＹｏｎｇｑｉａｎ（张永前）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎ...     

某大型水电枢纽坝基埋藏型岩溶发育特征及深层承压水研究

作者在现场工程地质勘察、试验基础上, 对我国西南某大型水电枢纽坝基所遇特殊的复杂埋藏型岩溶、承压水问题进行了研究, 弄清了坝基岩溶、承压水形成条件及发育特性, 对坝址选择及工程处理的决策具有重要意义。     

新疆下坂地水库坝基防渗墙试验研究

新疆下坂地水利枢纽工程地处高寒、高海拔的山区,坝基覆盖层厚度达147.95m,透水性强,易坍塌和漏浆,块石坚硬,坝基防渗处理难度罕见。针对这一工程问题进行了坝基防渗墙试验研究,结果表明,以大深度混凝土防渗墙为主墙,下接帷幕灌浆的墙幕结合方案。本文针对新疆下坂地深厚覆盖层坝基防渗墙进行了试验研究,找出了防渗墙有效的施工深度及合理的施工方法,从而为坝基防渗墙设计施工提供了可靠的依据。     

A piecewise-linearized algorithm based on the Krylov subspace for solving stiff ODEs

Numerical methods for solving Ordinary Differential Equations (ODEs) have received considerable attention in recent years. In this paper a piecewise-linearized algorithm based on Krylov subspaces for solving Initial Value Problems (IVPs) is proposed. MATLAB versions for autonomous and non-autonomous ODEs of this algorithm have been implemented. These implementations have been compared with other piecewise-linearized algorithms based on Padé approximants, recently developed by the authors of this paper, comparing both precisions and computational costs in equal conditions. Four case studies have been used in the tests that come from stiff biology and chemical kinetics problems. Experimental results show the advantages of the proposed algorithms, especially when the dimension is increased in stiff problems.     

完备格上基于Sup-T合成算子的矩阵的平方根

对于完备格L上给定的|I|×|I|的矩阵R,若存在|I|×|I|的L上的矩阵S满足S⊙S=R,则称S为R的平方根,其中I表示指标集|I|的基数,⊙在本文中指的是sup-T合成算子并且T是无限∨分配的保序的算子。本文给出了完备格上基于sup-T合成算子的矩阵平方根存在的充要条件以及相应的理论上的算法求解所有的平方根。     

On the N-wave equations and soliton interactions in two and three dimensions

Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann-Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic N-wave equations but mainly the 3- and 4-wave interactions are presented as examples. Their one and two-soliton solutions are derived and their soliton interactions are analyzed. It is shown that additional reductions may lead to new types of soliton solutions. In particular the 4-wave equations with ?₂ × ?₂ reduction group allow breather-like solitons. Finally it is demonstrated that RHP with sewing function depending on three variables t, x and y provides some special solutions of the N-wave equations in three dimensions.     

一类三阶拟线性发展方程的整体解

本文研究一类三阶拟线性发展方程ｕｔｔ－Δｕｔ＋ｕｔ＝ｎｉ＝１ｘｉσｉ（ｕｘｉ），（ｘ，ｔ）∈Ω×（０，Ｔ）的初边值问题，其中ΩＲｎ（ｎ≥１）为一有界域．证明了只要σｉ（ｓ）∈Ｃ１，σ′ｉ（ｓ）（ｉ＝１，…，ｎ）有界并且初始函数满足一定的条件，则上述问题存在唯一的整体弱解．     

一类半线性卷积积分微分方程的初边值问题

本文考虑具线性粘弹性杆受粘性阻尼的横振动所引出的积分微分方程的初边值问题，在某些条件下，得到了解的存在性、唯一性、稳定性和正则性的结论。     

非线性波动方程解的Blow up

本文主要讨论高维空间非线性波动方程的Ｃａｕｃｈｙ问题整体解的非存在性，我们证明对Ｕｕ－△ｕ＝ｆ（ｕ），ｆ（ｕ）＝ｃ｜ｕ｜ｐ－１ｕ，当１＜ｐ≥时，若初始能量非正，则无论初值数据的ｃｋ－范数（连续空间范数）多么小，解按Ｃｋ－范数或按Ｈｓ（Ｒｎ）（Ｓ≥１）都在有限时间内Ｂｌｏｗｕｐ，并且有相同的生命跨度．     

多阶段有补偿问题的非线性模型

通过对已有补偿问题的模型进行总结，抽象与升华，本文建立了Ｂａｎａｃｈ空间中一般形式多阶段有补偿随机规划问题的一个非线性模型，使已有所有的补偿问题均成为其特例；然后利用可测集值映射理论，正规凸的被积函数的性质及文［８」中的结论等，讨论了所给模型的适定性与其基本性质．