Inhalt des Dokuments
Differential Equations II A
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This lecture provides an introduction to boundary value problems for linear and nonlinear elliptic differential equations of second order. We will discuss Sobolev spaces, which rely on a generalized notion of differentiability, variational problems and the associated operator equations, monotone operators, Galerkin methods and linear finite elements as well as the Lax-Milgram lemma and the theorem of Zarantonello.
This 2-hour lecture will be held weekly and is worth 5 ECTS.
Tu | 12:30 pm - 2 pm | Lecture | online | Dr. Hans-Christian Kreusler |
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Mo | 2 pm - 4 pm | Exercise classes | online | André Eikmeier |
Secretariat | MA 568 | Alexandra Schulte |
Differential Equations III
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The subject of the lecture are initial boundary value problems for partial differential equations describing instationary processes. Using the variational approach and the theory of monotone operators, linear and nonlinear evolution equations of first and second order are studied.In addition to statements on the existence, uniqueness and stability of solutions, aspects of the approximate solution are also considered. Equations of fluid mechanics (Navier-Stokes equations, generalized Newtonian fluids) and elasticity theory and mechanics (vibrating membrane with damping) are considered as applications.
Bochner integral and Bochner-Lebesgue spaces, Gelfand triplets, Sobolev spaces for abstract functions, and compactness arguments for families of abstract functions (Lions-Aubin theorem and generalizations), among others, are provided as functional analytical foundations.
Tu | 11 am - 12:30 pm | Lecture | online | Dr. Hans-Christian Kreusler Dr. Robert Lasarzik |
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Fr | 2 pm - 4 pm | Exercise | online | Aras Bacho |
Secretary | MA568 | Alexandra Schulte |
Das Seminar richtet sich an Studierende, die eine Bachelor- oder Masterarbeit anfertigen wollen.
Das Seminar findet online als Blockseminar am
Freitag, den 2. Juli 2021 und Samstag, den 3. Juli 2021
statt.
Eine erste Vorbesprechung findet am Montag, den 19. April 2021 ab 16:15 Uhr via "zoom" statt.
Die Zugangsdaten lauten:
https://tu-berlin.zoom.us/j/64672811761?pwd=MEpXRlZ2bEJib1diOFBnRjB3UUxYZz09
Meeting-ID: 646 7281 1761
Kenncode: 042258
Voraussetzungen:
Möglichst Differentialgleichungen I und II A oder vergleichbare Kenntnisse (Differentialgleichungen II A kann parallel im laufenden Semester gehört werden.)
Für weitere Fragen stehen Ihnen Frau Schulte (secr_diffeqs@math.tu-berlin.de) zur Verfügung.