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Module Number:
| 14500
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| Module Title: | Evolution Equations - Nonlinear Semigroups |
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Evolutionsgleichungen - Nichtlineare Halbgruppen
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| Department: |
Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
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| Responsible Staff Member: | -
Prof. Dr. rer. nat. habil. Hauer, Daniel
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| Language of Teaching / Examination: | English |
| Duration: | 1 semester |
| Frequency of Offer: |
On special announcement
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| Credits: |
8
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| Learning Outcome: | After successfully completing the module, students have extensive knowledge of functional analytical methods for solving non-linear evolution equations and their regularity. |
| 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
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| Recommended Prerequisites: | Knowledge of the content of the modules
- 11103: Analysis I
- 11104: Analysis II
- 11201: Analysis III
- 11303: Funktionalanalysis oder 13844: Functional Analysis
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| Mandatory Prerequisites: | None |
| Forms of Teaching and Proportion: | -
Lecture
/ 4 Hours per Week per Semester
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Exercise
/ 2 Hours per Week per Semester
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Self organised studies
/ 150 Hours
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| Teaching Materials and Literature: | - 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.
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| Module Examination: | Final Module Examination (MAP) |
| Assessment Mode for Module Examination: | - Oral examination, 30 min.
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| Evaluation of Module Examination: | Performance Verification – graded |
| Limited Number of Participants: | None |
| Part of the Study Programme: | -
Master (research-oriented) /
Angewandte Mathematik /
PO 2019
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| Remarks: | - Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Kombinatorik“
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| Module Components: | - Lecture: Nonlinear Semigroups
- Accompanying exercises
- Related examination
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| Components to be offered in the Current Semester: | |
