On nonlinear evolution variational inequalities involving variable exponent | Zendy

Mingqi Xiang | Zendy

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On nonlinear evolution variational inequalities involving variable exponent

Author(s) -

Mingqi Xiang

Publication year - 2013

Publication title -

electronic journal of qualitative theory of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.524

H-Index - 33

ISSN - 1417-3875

DOI - 10.14232/ejqtde.2013.1.72

Subject(s) - mathematics , nonlinear system , exponent , inequality , variable (mathematics) , variational inequality , mathematical analysis , pure mathematics , statistical physics , physics , philosophy , linguistics , quantum mechanics

In this paper, we discuss a class of quasilinear evolution variational inequalities with variable exponent growth conditions in a generalized Sobolev space. We obtain the existence of weak solutions by means of penalty method. Moreover, we study the extinction properties of weak solutions to parabolic inequalities and provide a sufficient condition that makes the weak solutions vanish in a finite time. The existence of global attractors for weak solutions is also obtained via the theories of multi-valued semiflow.

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