EVOLUTION PROBLEMS ASSOCIATED WITH PRIMAL LOWER NICE FUNCTIONS AND APPLICATIONS TO CONTROL THEORY.
Sylvie Marcellin · 2007
In a general Hilbert space H, given a smooth function f from an open subset O of H into R, nonlinear ordinary difierential equations (ODEs for short) of the form i_ u(t) = rf(u(t)); t ‚ T0; with initial value u(T0)=u02O, also known as the steepest descent problem, have been widely studied because of their crucial interest in mechanics, physics, and optimization, especially when f is supposed to be convex. Dropping the smoothness and involving extended real valued proper lower semicontinuous (lsc) convex functions, several authors investigated the existence and further properties of locally absolutely continuous solutions of the difierential inclusion _ u(t) + @f(u(t)) 3 0 a.e., with u(0) = u0 and f(u0) < +1;