This book presents a detailed and contemporary account of the
classical theory of convergence of semigroups and its more recent
development treating the case where the limit semigroup, in
contrast to the approximating semigroups, acts merely on a subspace
of the original Banach space (this is the case, for example, with
singular perturbations). The author demonstrates the far-reaching
applications of this theory using real examples from various
branches of pure and applied mathematics, with a particular
emphasis on mathematical biology. The book may serve as a useful
reference, containing a significant number of new results ranging
from the analysis of fish populations to signaling pathways in
living cells. It comprises many short chapters, which allows
readers to pick and choose those topics most relevant to them, and
it contains 160 end-of-chapter exercises so that readers can test
their understanding of the material as they go along.
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