For more than forty years, the equation y (t) = Ay(t) + u(t) in
Banach spaces has been used as model for optimal control processes
described by partial differential equations, in particular heat and
diffusion processes. Many of the outstanding open problems,
however, have remained open until recently, and some have never
been solved. This book is a survey of all results know to the
author, with emphasis on very recent results (1999 to date).
The book is restricted to linear equations and two particular
problems (the time optimal problem, the norm optimal problem) which
results in a more focused and concrete treatment. As experience
shows, results on linear equations are the basis for the treatment
of their semilinear counterparts, and techniques for the time and
norm optimal problems can often be generalized to more general cost
functionals.
The main object of this book is to be a state-of-the-art monograph
on the theory of the time and norm optimal controls for y (t) =
Ay(t) + u(t) that ends at the very latest frontier of research,
with open problems and indications for future research.
Key features:
. Applications to optimal diffusion processes.
. Applications to optimal heat propagation processes.
. Modelling of optimal processes governed by partial
differential equations.
. Complete bibliography.
. Includes the latest research on the subject.
. Does not assume anything from the reader except
basic functional analysis.
. Accessible to researchers and advanced graduate
students alike
. Applications to optimal diffusion processes.
. Applications to optimal heat propagation processes.
. Modelling of optimal processes governed by partial
differential equations.
. Complete bibliography.
. Includes the latest research on the subject.
. Does not assume anything from the reader except
basic functional analysis.
. Accessible to researchers and advanced graduate
students alike"
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