Sciences and Technologies Team(ESTE),Abstract We consider nonlinear parabolic problems in a variational framework.The leading part is a monotone operator whose growth is controlled by time-and space-dependent Musielak...Sciences and Technologies Team(ESTE),Abstract We consider nonlinear parabolic problems in a variational framework.The leading part is a monotone operator whose growth is controlled by time-and space-dependent Musielak functions.On Musielak's controlling functions we impose regularity conditions which make it possible to extend certain classical results such as the density of smooth functions,a Poincar′e-type inequality,an integration-by-parts formula and a trace result.Bringing together these results,we adapt the classical theory of monotone operators and prove the well-posedness of the variational problem.展开更多
文摘Sciences and Technologies Team(ESTE),Abstract We consider nonlinear parabolic problems in a variational framework.The leading part is a monotone operator whose growth is controlled by time-and space-dependent Musielak functions.On Musielak's controlling functions we impose regularity conditions which make it possible to extend certain classical results such as the density of smooth functions,a Poincar′e-type inequality,an integration-by-parts formula and a trace result.Bringing together these results,we adapt the classical theory of monotone operators and prove the well-posedness of the variational problem.
基金Li Baode is supported by NSFC(No.11461065,No.11161044)Scientific Research Projects in Colleges and Universities in Xinjiang Uyghur Autonomous Region(No.XJEDU2014S001)
