Lehrinhalte
depending on topic,
examples include:
- conservation equations
- stochastic PDEs
- geo-physical flows
- free boundary value problems
- chemotaxis
- Besov spaces
- pseudo differential operators
[u]Contents Parabolic differential equations:[/u]
We will study basic properties of linear and semilinear parabolic equations, in particular
explicit classical solutions to the heat equation; existence and uniqueness of solutions to semilinear parabolic equations; qualitative properties of solutions (e.g. maximum principles, regularity, asymptotic behavior, blow-up)
Literatur
depending on topic
[u]here:[/u]
Evans: Partial Differential Equations (AMS),
Lieberman: Second Order Parabolic Differential Equations (World Scientific),
Renardy, Rogers: An Introduction to Partial Differential Equations (Springer)
Voraussetzungen
recommended: depending on topic, typically Functional Analysis
[u]here:[/u]
Analysis and Linear Algebra, Ordinary Differential Equations, Integration Theory, basic knowledge in Functional Analysis
Zusätzliche Informationen
This course can be taken in parallel to the lecture Partial Differential Equations I and overlapping contents will be avoided as far as possible.
Online-Angebote
moodle
depending on topic,
examples include:
- conservation equations
- stochastic PDEs
- geo-physical flows
- free boundary value problems
- chemotaxis
- Besov spaces
- pseudo differential operators
[u]Contents Parabolic differential equations:[/u]
We will study basic properties of linear and semilinear parabolic equations, in particular
explicit classical solutions to the heat equation; existence and uniqueness of solutions to semilinear parabolic equations; qualitative properties of solutions (e.g. maximum principles, regularity, asymptotic behavior, blow-up)
Literatur
depending on topic
[u]here:[/u]
Evans: Partial Differential Equations (AMS),
Lieberman: Second Order Parabolic Differential Equations (World Scientific),
Renardy, Rogers: An Introduction to Partial Differential Equations (Springer)
Voraussetzungen
recommended: depending on topic, typically Functional Analysis
[u]here:[/u]
Analysis and Linear Algebra, Ordinary Differential Equations, Integration Theory, basic knowledge in Functional Analysis
Zusätzliche Informationen
This course can be taken in parallel to the lecture Partial Differential Equations I and overlapping contents will be avoided as far as possible.
Online-Angebote
moodle
- Lehrende: StinnerChristian
Semester: WT 2018/19