A Class of Parabolic Hemivariational Inequalities
-
摘要: 研究一类拟线性抛物型H-半变分不等式,即研究具有非凸、非光滑泛函的抛物型变分不等式。这类问题的研究来自力学。利用Clarke广义梯度和伪单调算子理论,证明了一类拟线性抛物型H-半变分不等式解的存在性。
-
关键词:
- 抛物型H-半变分不等式 /
- 多值映象 /
- 存在性结果
Abstract: Quasilinear parabolic hemivariational inequalities as a generalization to nonconvex functions of the parabolic variational inequalities are discussed.This extension is strongly motivated by various problems in mechanics.By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators,it is proved there exists at least one soluton. -
[1] Zeidler E. Nonlinear Functional Analysis and Its Applications[M]. ⅡA and ⅡB. New York-Berlin-Heidelberg: Springer-Velag,1990. [2] 张石生. 变分不等式和相补问题理论及应用[M]. 上海:上海科技出版社,1991. [3] ZHANG Cong-jun, ZHANG Shi-sheng. On recent developments and some open questions in the study of Browder-Hartman-Stampaccia variational inequality[J]. J Math Research and Exposition,1995,15(3):313-317. [4] 王耀东. 变分不等方程[M]. 北京: 高等教育出版社,1987. [5] LIU Zhen-hai. Nonlinear evolution variational inequalities with nonmonotone perturbations[J]. Nonlinear Analysis,1997,29(11):1231-1236. [6] 刘振海. 拟线性椭圆系统的H-半变分不等式[J]. 系统工程,1996,14(6):63-65. [7] 刘振海. 拟线性椭圆型H-半变分不等式[J]. 应用数学和力学,1999,20(2):211-216. [8] Panagiotopoulos P D. Hemivariational inequalities[A]. Applications in Mechanics and Engineering[M]. Berlin: Springer-Verlag,1993. [9] Panagiotopoulos P D. Coercive and semicoercive hemivariational inequalities[J]. Nonlinear Analysis,1991,16:209-231. [10] Miettinen M. A parabolic hemivariational inequality[J]. Nonlinear Analysis,1996,26(6):725-734. [11] 张恭庆. 临界点理论及其应用[M]. 上海:上海科技出版社,1986. [12] Clarke F H. Optimization and Nonsmooth Analysis[M]. New York: Wiley,1983. [13] LIU Zhen-hai. Nonlinear degenerate parabolic equations[J]. Acta Math Hungar,1997,77(1-2):147-157. [14] Ton B A. Nonlinear evolution equations in Banach spaces[J]. J Differential Equations,1971,9(3):608-618. -
计量
- 文章访问数: 2113
- HTML全文浏览量: 76
- PDF下载量: 690
- 被引次数: 0
下载:
渝公网安备50010802005915号