期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1977
卷号：74
期号：10
页码：4150-4151
DOI：10.1073/pnas.74.10.4150
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：The paper deals with hyperbolic homogeneous systems [Formula: see text] of partial differential equations with constant coefficients for an N-vector u(t,x1...,xn). Here, P is a matrix form of order N and degree m. In the scalar case (N = 1), every hyperbolic P is limit of strictly hyperbolic ones. This does not hold for systems as is shown here for the special case N = n = 3, m = 2. Assuming P(1,0...,0) to be the unit matrix, we represent P by a point in R81. The hyperbolic P form a closed set H in R81, the strictly hyperbolic ones an open subset Hs of H. An example is given for a P in H which is not in the closure of Hs. Moreover, it is shown that near that P the set H coincides with an algebraic manifold of codimension 4.
关键词：hyperbolicity ; systems of differential equations
