On some differential inclusions and their applications
Vol. 1 (1994), No. 2, Page 369--391.
Åukaszewicz, Grzegorz ; Ton, Bui An
On some differential inclusions and their applications
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
The existence of a solution of the evolution inclusion % u' + \partial Ï(t,u) + g(t,u)-F(u) \ni 0 \ \ \text{on}\ \ (0,T), u(0)=ξ % is established. For each t in [0,T], Ï (t, \cdot) is a proper l.s.c. convex function from H to [0, \infty] \; and F is an upper hemicontinuous set-valued mapping of L^2(0,T;H) into its closed convex subsets. The time periodic problem % u' + \partial Ï(t,u)-F(u) \ni 0 \ \ \text{on}\ \ (0,T), \ \ u(0)=u(T) % is studied. Applications to the heat equation with mixed boundary conditions and to the coupled Navier Stokes and heat equations with convection, dissipation and control terms in non-cylindrical domains are given.
Mathematics Subject Classification (1991): Primary 47H04, 35K55; Secondary 35K20, 35R70
Mathematical Reviews Number: MR1317465
Received: 1993-08-05
