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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Partial Differential Equations I SemesterSoSe 2025 Lecturer Georg Dolzmann Type of course (Veranstaltungsart) Vorlesung German title Partielle Differentialgleichungen I Contents Diese Vorlesung bietet eine erste Einführung in die Theorie der partiellen Differentialgleichungen. Sie wird im Wintersemester mit der Vorlesung Partielle Differentialgleichungen II fortgesetzt. Es werden zunächst die wichtigsten Gleichungen hergeleitet, anschließend wird der moderne funktionalanalytische Zugang besprochen. Schwerpunkte sind Sobolevräume, schwache Formulierungen, Regularitätstheorie, Maximumprinzipien, Greensche Funktionen. This lecture provides a first introduction into modern methods in partial differential equations and will be continued during the Fall/Winter Term 2025/26. Topics include: How do we describe (physical) systems with partial differential equations. What is a conservation law, a heat equation, or a wave equation? What is a solution? Can we prove existence of solutions and what are the qualitative properties of the solutions? The main focus will be the fundamental concept of weak solutions in Sobolev spaces but we will also touch upon classical approaches like series expansions and Green's functions. Literature Evans, L.C., Partial Differential Equations, American Mathematical Society. Gilbarg, D., Trudigern, N.S., Elliptic Partial Differential Equations of Second Order, Springer Verlag. Jost, J., Partielle Differentialgleichungen, Springer Verlag. Renardy, M., Rogers, R., An Introduction to Partial Differential Equations, Springer Verlag. Schweizer, B., Partielle Differentialgleichungen, Springer Verlag. Recommended previous knowledge Analysis I-III. Die Vorlesungen Analysis IV und Funktionalanalysis sind nicht notwendig aber hilfreich. Calculus of several variables. Basic knowledge of functional analysis and integral theorems is useful but not required. We will review Gauss' theorem for sufficiently smooth sets in n-dimensional Euclidean spaces (usually covered in Analysis IV) and basic Hilbert space theory for the definition of weak solutions. The main existence theorem (Lax Milgram) is not part of the class on functional analysis and will be proven in Partial Differential Equations 1. This class (and the successive class Partial Differential Equations 2) can be taken without having taken a class on functional analysis. However, it is strongly recommended to take (concurrently) the class on functional analysis during the Fall/Winter term if you want to take Partial Differential Equations 2. Time/Date Mi 10-12, Do 8-10 Location Mi M 104, Do H 31 Additional question session Time/Date: Recitatiton Section Mi 8-10 Location: M 101 Course homepage https://elearning.uni-regensburg.de/course/view.php?id=69477 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, MV, MAngAn, CS-M-P1, CS-M-P2, PHY-B-WE03, PHY-M-VE03 ECTS 9 LP |