Beyond partial differential equations
“Although the text was written for truly advanced graduate students, it contains a wealth of well presented results on semigroup theory and the theory of evolution equations with applications to hyperbolic equations and systems and will therefore serve as a valuable resource for researchers in mathematics and theoretical physics as well,” reads Thomas Hagen's review of the book “Beyond partial differential equations. On linear and quasi-linear abstract hyperbolic evolution equations.” by Horst Reinhard Beyer [Lecture Notes in Mathematics 1898. Berlin: Springer. (2007; Zbl 1144.35001)].
“The main appeal of the monograph to researchers is twofold. On the one hand the text is abound with nontrivial examples of semigroups and evolution operators from hyperbolic problems in physics and is thus quite different from standard texts on analytic semigroups or typical problems arising in fluid dynamics or engineering. On the other hand the monograph provides a self-contained introduction into the important and very general theory of abstract evolution equations, which brings powerful analytical tools for the study of hyperbolic problems to the fore.”