Unboundedness of solutions and comparison theorems for time-dependent quasilinear differential matrix inequalities
Unboundedness of solutions and comparison theorems for time-dependent quasilinear differential matrix inequalities
复制标题
时变拟线性微分矩阵不等式解的无界性和比较定理
DOI：
10.1016/0022-0396(73)90042-9
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发表时间：
1973
影响因子：
2.4
通讯作者：
E. C. Young
中科院分区：
文献类型：
--
作者：
C. Y. Chan;E. C. Young
本文关注与时间相关的拟线性微分系统解的无界性以及此类系统的比较定理。在标量情况下，McNabb [1] 和 Dunninger [2] 在与我们不同的假设下获得了类似的结果。在第 3 节中，给出了示例来说明我们的结果。令 52 为 n 维欧几里得空间 En 中的有界域，D 为其具有分段平滑边界 asl 的闭包，H 为 Em 中包含“原点”的域。还令 x 表示点 (x1,..., x, J of 8, D 表示对 xi, i= l,..., 11 的微分。用 R 表示柱面 ((3, t)(x E J2, t> 0})，用 w 表示柱面 ((x, t) 1 x ED, t> O}。用 1 表示微分算子
This paper is concerned with the unboundedness of solutions of timedependent quasilinear differential systems and with comparison theorems for such systems. In the scalar case, analogous results were obtained by McNabb [l] and Dunninger [2] under different hypotheses from ours. In Section 3, examples are given to illustrate our results. Let 52 be a bounded domain in n-dimensional Euclidean space En, D be its closure with piecewise smooth boundary asl, and H be a domain in Em containing ‘the origin. Also let x denote a point (x1,..., x, J of 8, and D, indicate differentiation with respect to xi, i= l,..., 11. Denote by R the cylinder ((3, t)(x E J2, t> 0} and by w the cylinder ((x, t) 1 x ED, t> O}. Let 1 denote the differential operator