University Calendar: Loyola University Chicago

November 21, 2022
11:00 AM - 12:00 CST
Xiang Wan, xwan1@luc.edu
BVM 506
Open to the public.
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Speaker: Xiang Wan, Loyola University Chicago
Title: Operator Semigroups and Applications to Differential Equations, Part III
Abstract: In Part II, we've introduced the theoretic-applauded Hille-Yosida Theorem and its variants which characterize the type of (unbounded) operators that generate s.c.-semigroups, which is the answer we seek for to the Abstract Cauchy Problems (ACP).
In this talk, we will introduce a more practical result which, unlike Hille-Yosida, doesn't involve conditions on infinite many resolvents. Rather, dissipativity of the operator A and surjectivity of a resolvent are proven to be critical (Lumer-Phillips). We will then see how it works with several concrete examples that can be formed as ACPs.