The present work may be inscribed as a contribution to the general effort of research
in nonsmooth optimization problems associated with nonlinear partial differential equations.
More precisely, the main aim of these notes is to examine distributed control
problems governed by nonlinear evolution equations (parabolic or hyperbolic), in the absence of
differentiability properties. In this setting, a special emphasis is given to nonlinear hyperbolic
problems which are less discussed in the literature.
In order to obtain a more complete image of the area of research we have mentioned
and to show other possible applications of the methods, several sections deal with problems
which don't enter strictly in the announced subject: nonlinear delay differential equations,
boundary control, elliptic problems and optimal design.
The material of the book is divided into three parts, after the type of the nonlinear
term which occurs in the state system: semilinear and quasilinear problems, variational
inequalities, free boundary problems. Among the different topics underlined throughout the work,
we refer to: existence of optimal pairs, first order necessary conditions, general and efficient
approximation procedures. Each time when this is possible, we indicate applications to regularity
or bang-bang results for the optimal control. Examples clarifying and motivating the theory are
included in every chapter.