PROGRESSING WAVE SOLUTIONS TO QUASI-LINEAR SYSTEMS MIXED PROBLEMS

ＰＲＯＧＲＥＳＳＩＮＧＷＡＶＥＳＯＬＵＴＩＯＮＳＴＯＱＵＡＳＩ－ＬＩＮＥＡＲＳＹＳＴＥＭＳＭＩＸＥＤＰＲＯＢＬＥＭＳ￥ＷＡＮＧＷＥＩＫＥ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００７２，Ｃｈｉｎ...     

P阶线性偏微分方程组柯西问题的解析解的一般表达式

本文是在[1]—[10]工作的基础上,在复域中讨论P阶线性偏微分方程组柯西问题 (方程中m=∞时,级数在原点附近一致收敛)解析解的结构,获得了方程组的系数矩阵B_4(0)(i=1,2,…,p-1)及微分算子D之间的相互可易,部分可易和互不可易的诸情况下的一般解析解的级数形式显式表达式。     

一类具重特征线性偏微分算子的局部可解性

运用Ｇａｒｄｉｎｇ不等式和Ｆｅｆｅｒｍａｎ－Ｐｈｏｎｇ不等式，建立了一类具实主会征的线性偏微分算子的局部可解性。     

On High-Frequency Soliton Solutions to a （2＋1）-Dimensional Nonlinear Partial Differential Evolution Equation

A （2＋1）-dimensional nonlinear partial differential evolution （NLPDE） equation is presented as a model equation for relaxing high-rate processes in active barothropic media. With the aid of symbolic computation and Hirota＇s method, some typical solitary wave solutions to this （2＋1）-dimensional NLPDE equation are unearthed. As a result, depending on the dissipative parameter, single and multivalued solutions are depicted.     

THE δ^－－PROBLEM FOR HOLOMORPHIC （0,2）－FORMS ON PSEUDOCONVEX DOMAINS IN SEPARABLE HILBERT SPACES AND D.F.N. SPACES

This paper shows that the δ^--problem for holomorphic (0, 2)-forms on Hilbert spaces is solv-able on pseudoconvex open subsets. By using this result, the authors investigate the existence ofthe solution of the δ^--equation for holomorphic(0, 2)-forms on pseudoconvex domains in D.F.N.spaces.