From 15th ISeminar 2011/12 Operator Semigroups for Numerical Analysis
this week we reached the last big theoretical lecture of this seminar. After this hard lecture we will turn our attention to more "numerical analysis" topics like operator splitting and rational approximations. But before that, we have to face analytic semigroups.
Parabolic equations play a special role in the theory of partial differential equations: they enjoy lots of good properties. The most important one is that they smooth out every initial function and the solutions become smooth in space and in time. If we try to generalise parabolic equations to the abstract Cauchy problem level, we arrive at analytic semigroups and sectorial operators. You can read more about this at the pdf-link below.
We kindly ask the teams of Bern and Bogota to create the official solutions for this lecture.
Best wishes and good reading,
your virtual lecturers
A corrected version will be uploaded soon, until then see:
Discussion of Lecture 9.
Solutions and discussion of the exercises.
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