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Recently started to study Semigroup Theory. My background is equivalent to the first three chapters of the Jack Hale's book, Asymptotic Behavior of Dissipative Systems. Looking for a reference to an article in the law. It may be a review, but contains interesting results for a beginner, and also with some possible research topics.

Thanks Advance,

Juan Valdez

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    $\begingroup$ Do you know Pazy? $\endgroup$ – timur Sep 22 '11 at 17:02
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As mentioned by Timur, one classic reference is Pazy, where you can read of the classic results (till around 1980).

An excellent book is Engel and Nagel, which contains lots of applications and recent results.

If you are interested in particular in parabolic problems, then Lunardi is a standard reference.

As a start, I recommend the short version of Engel and Nagel, which is an excellent reading.

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I really like Brian Davies's "One parameter semigroups": it is short and well written. It does mostly focus on $C_0$-semigroups and not so much on analytic semigroups.

Then there's also the book by the old master, Yosida's "Functional analysis" which has a chapter on semigroup theory. His notations are a bit old-fashioned by now, but it's still an excellent reference book.

For an extremely short introduction to $C_0$ and analytic semigroups, see also Chapter 4 in my SPDE lecture notes.

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I agree that Pazy's is definitely a classic. In graduate school I recall reading parts of a very nice book by Aldo Belleni-Morante, "Applied Semigroups and Evolution Equations" (1979). The first part of this book contains numerous examples, detailed calculations, etc. (Just looking now, there is also "Applied Nonlinear Semigroups: An Introduction" by A. Belleni-Morante and A. C. McBride (1998).)

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