Existence of Solutions for Parabolic Type Evolution Differential Inclusions and the Property of the Solution Set

Wang Zhihua

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(3): 314-318

Wang Zhihua. Existence of Solutions for Parabolic Type Evolution Differential Inclusions and the Property of the Solution Set[J]. Applied Mathematics and Mechanics, 1999, 20(3): 314-318.

Citation:

Wang Zhihua. Existence of Solutions for Parabolic Type Evolution Differential Inclusions and the Property of the Solution Set[J]. Applied Mathematics and Mechanics, 1999, 20(3): 314-318.

Citation:

Wang Zhihua. Existence of Solutions for Parabolic Type Evolution Differential Inclusions and the Property of the Solution Set[J]. Applied Mathematics and Mechanics, 1999, 20(3): 314-318.

PDF( 1965 KB)

Existence of Solutions for Parabolic Type Evolution Differential Inclusions and the Property of the Solution Set

Wang Zhihua

Department of Business & Economy, Shangdong Electrical Power College, Jinan 250002, P. R. China

Received Date: 1997-11-22
Rev Recd Date: 1998-12-05
Publish Date: 1999-03-15

Abstract

Abstract

In this paper, parabolic type differential inclusions with time dependenoe are discussed and this problem is related to the study of the nonlinear distributed parameter control systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J.P.Aubin et al are generalized and improved.
- evolution operator,
- set-valued map,
- differential inclusion,
- mild-solution,
- fixed-point theorem

FullText(HTML)

References(7)

References

[1]	Aubin J P,Cellina A.Differential Inclusions[M].Berlin:Springer-Verlag,1984.
[2]	Frankowska H.Estimations a priori pour les inclusions differentielles operationelles[J].C R Acad Sci Paris,1989,308(5):47～50
[3]	Xue X,Song G.Existence results of mild solutions to semilinear evolution inclusions in Banach spaces[J].Northeast Math J,1995,11(7):151～156
[4]	Vrabie V V.Some compactness methods in the theory of nonlinear evolution equations to P D E[J].Banach Centre Publ,1987,19(7):351～360
[5]	Wagner D.Survey of measurable selection theorems[J].SIAM J Control and Optim,1977,15(3):859～903
[6]	周鸿兴,王连文.线性算子半群理论及应用[M].济南:山东科学技术出版社,1994.
[7]	Aubin J P,Ekeland I.Applied Nonlinear Analysis[M].New York:Wiley Sons,1984