The book contains a unitary and systematic presentation of both
classical and very recent parts of a fundamental branch of
functional analysis: linear semigroup theory with main emphasis on
examples and applications. There are several specialized, but quite
interesting, topics which didn't find their place into a monograph
till now, mainly because they are very new. So, the book, although
containing the main parts of the classical theory of Co-semigroups,
as the Hille-Yosida theory, includes also several very new results,
as for instance those referring to various classes of semigroups
such as equicontinuous, compact, differentiable, or analytic, as
well as to some nonstandard types of partial differential
equations, i.e. elliptic and parabolic systems with dynamic
boundary conditions, and linear or semilinear differential
equations with distributed (time, spatial) measures. Moreover, some
finite-dimensional-like methods for certain semilinear
pseudo-parabolic, or hyperbolic equations are also disscussed.
Among the most interesting applications covered are not only the
standard ones concerning the Laplace equation subject to either
Dirichlet, or Neumann boundary conditions, or the Wave, or
Klein-Gordon equations, but also those referring to the Maxwell
equations, the equations of Linear Thermoelasticity, the equations
of Linear Viscoelasticity, to list only a few. Moreover, each
chapter contains a set of various problems, all of them completely
solved and explained in a special section at the end of the book.
The book is primarily addressed to graduate students and
researchers in the field, but it would be of interest for both
physicists and engineers. It should be emphasised that it is almost
self-contained, requiring only a basic course in Functional
Analysis and Partial Differential Equations.
General
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