Evolution Equations - Nonlinear Semigroups
Evolutionsgleichungen - Nichtlineare Halbgruppen
8 CPirregularlyEN
Prerequisites
Recommended, as written
Knowledge of the content of the modules • 11103: Analysis I • 11104: Analysis II • 11201: Analysis III • 11303: Funktionalanalysis oder 13844: Functional Analysis
Contents
• Geometry of Banach spaces • Accretive operators • Existence of semigroups • Regularisation effect of solutions to gradient systems • Abstract Sobolev and Gagliardo-Nirenberg inequalities • L1-L∞ Regularisation effect
Learning outcomes
After successfully completing the module, students have extensive knowledge of functional analytical methods for solving non-linear evolution equations and their regularity.
Assessment
• Oral examination, 30 min.
Literature (4)
- E. Emmrich, Gewöhnliche und Operator-Differentialgleichungen, Eine integrierte Einführung in Randwertprobleme und Evolutionsgleichungen für Studierende, Vieweg+Teubner Verlag Wiesbaden, 2004.
- H.W. Alt, Linear Funktionalanalysis, Eine anwendungsorientierte Einführung, Springer Berlin, Heidelberg, 2012.
- V. Barbu, Nonlinear Differential Equations of Monotone Types in Banach Spaces, Springer Monographs in Mathematics, 2010.
- Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, AMS, Mathematical Surveys and Monographs, Vol. 49, 1997.
Remarks
• Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Kombinatorik“
Source: BTU's module description · retrieved 29 Sep 2026Original