Existence and uniqueness of distributed optimal control problems governed by parabolic variational inequalities of the second kind

M. BOUKROUCHE; D.A. TARZIA

Bahia Blanca

Congreso; III MACI 2011 - III Congreso de Matemática Aplicada, Computacional e Industrial; 2011

ASAMACI - Asociación Argentina de Matemática Aplicada, Computacional e Industrial

Let $u_{g}$ be the unique solution of a parabolic variationalinequality of second kind, with a second member $g$. Using aregularization method, we prove,  for all  $g_{1}$ and $g_{2}$,   amonotony property  between $\mu u_{g_{1}} + (1-\mu)u_{g_{2}}$  and$u_{\mu g_{1} + (1-\mu)g_{2}}$ for $\mu \in [0 , 1]$. This  allowedus to prove the existence and uniqueness results to a family ofdistributed optimal control problems governed by parabolicvariational inequalities of second kind over $g$ for each heattransfer coefficient $h>0$, associated to the Newton law, and ofanother distributed optimal control problem associated to aDirichlet boundary condition.