EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS

doi:10.1016/S0252-9602(11)60355-X

Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (5): 1709-1718.doi: 10.1016/S0252-9602(11)60355-X

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EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS

PENG Zi-Jia, LIU Yi-Liang^*

School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China|Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, China

Received:2010-09-02 Online:2011-09-20 Published:2011-09-20
Contact: LIU Yi-Liang,yiliangliu100@126.com E-mail:pengzijia@126.com; yiliangliu100@126.com
Supported by:
Project supported by NSFC (10971019), Scientific Research Fund of Guangxi Education Department (201012MS067) and Hunan Provincial Innovation Foundation For Postgrad-uate (CX2010B117).

Abstract

Abstract:

This paper deals with the initial-value problem of nonlinear evolution inclu-sions of the form dB(u)/dt + A(u) ∋ f, v₀ ∈ B(u)(0), where the operator B is induced by a subgradient and A is pseudomonotone. Existence theorem is established via the time discretization technique and the regularization method. In contrast to the previous results, here we impose a weaker coerciveness condition on A and remove the strong monotonicity from B.

Key words: time-discretization, pseudomonotone operator, regularization

CLC Number:

35K15

PENG Zi-Jia, LIU Yi-Liang. EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS[J].Acta mathematica scientia,Series B, 2011, 31(5): 1709-1718.

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EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS

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