Below you can see a list of past talks at the Proof Mining Seminar. For forthcoming talks, see the main page.
Wednesday, January 11, 2023
Nicholas Pischke (TU Darmstadt)
A proof-theoretic metatheorem for nonlinear semigroups generated by an accretive operator and applications
Abstract:
Already since the pioneering studies of Browder and Kato, a major tool in the study of nonlinear evolution equations has been the theory of nonlinear semigroups and their generators, with the latter in particular linking to the theory of accretive operators via nonlinear analogues of the Hille-Yosida theorem. One of the most important basic results in that context is the representation theorem due to Crandall and Liggett of the semigroup associated with the classical Cauchy problem for a given set-valued accretive operator over a Banach space. I discuss how proofs involving those semigroups can be treated in higher type arithmetic such that proof mining metatheorems are still available. This in particular requires a treatment of the dual formulation of the notion of accretivity together with other substantial extensions of the previous intensional framework for accretive operator theory. Lastly, I will illustrate the applicability of this metatheorem by presenting a particular case study for a result due to Simeon Reich on the asymptotic behavior of these semigroups.