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Partial Differential Equations [MA3005] - WS 19/20

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The lectures will be an introduction to the theory of Partial Differential Equations (PDEs). They will cover the following topics: classical solutions to Laplace, heat and wave equations, first order PDEs, Sobolev spaces, weak solutions to second order elliptic PDEs.

Prerequisites: MA1001 Analysis 1, MA1002 Analysis 2, MA2003 Measure and Integration, MA2004 Vector Analysis.

Literature: L.C.Evans, Partial Differential Equations, Graduate Studies in Mathematics Vol. 19, AMS, 1998.

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Timetable

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Lectures: Mondays and Fridays 12:15-14:00, MI HS 3.

Exercise class:

Course Material

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Handwritten lecture notes will be uploaded here every week.

Topic
Week 1: Introduction and heat equation in 1D Lectures 1-2
Week 2: Heat equation in nD maximum principles Lectures 3-4
Week 3: Solution formula for the heat equation in R^n Lecture 5
Week 4: Laplace and Poisson equation in R^n Lectures 6-7
Week 5: Properties of harmonic functions Lectures 8-9
Week 6: Poisson kernel and Green function method Lectures 10-11
Week 7: Scalar conservation laws: characteristics, regular solutions, rarefaction, shocks Lectures 12-13
Week 8: Scalar conservation laws: weak solutions Lectures 14-15
Week 9: Scalar conservation laws: Rankine-Hugoniot condition, entropy solutions Lectures 16-17
Week 9: Scalar conservation laws: Rankine-Hugoniot condition, entropy solutions Lectures 16-17
Week 10: Sobolev Spaces: First properties and approximation by smooth functions Lectures 18-19
Week 11: Sobolev Spaces: Extensions and Traces Lectures 20-21
Week 12: Sobolev Spaces: Sobolev and Poincare inequalities, embeddings Lectures 22-23
Week 13: Second order elliptic PDEs: weak solutions Lectures 24-25
Week 14: Second order elliptic PDEs: maximum principles Lectures 26-27

   Exercise Sheet    Comments   Proposed solutions  
Class 1 Sheet 1   Solution Sheet 1
Class 2 Sheet 2   Solution Sheet 2
Class 3 Sheet 3   Solution Sheet 3
Class 4 Sheet 4   Solution Sheet 4
Class 5 Sheet 5 No changes compared to the draft version Solution Sheet 5
Class 6 Sheet 6 No changes compared to the draft version Solution Sheet 6
Class 7 Sheet 7 No changes compared to the draft version Solution Sheet 7
Class 8 Sheet 8 No changes compared to the draft version Solution Sheet 8
Class 9 Sheet 9   Solution Sheet 9
Class 10 Sheet 10   Solution Sheet 10
Class 11 Sheet 11   Solution Sheet 11
Class 12 Sheet 12   Solution Sheet 12
Class 13 Sheet 13   Solution Sheet 13

People

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  Name eMail Office Consultation
Lecturer:   Marco Cicalese  cicalesema.tum.de   MI 03.08.038   lecture break; after lecture
Group Mo. 14:15-15:45 :   Mi-Song Dupuy   dupuyma.tum.de   MI 03.08.021    
Group Tu. 10:15-11:45 :   Marwin Forster   marwin.forsterma.tum.de   MI 03.08.040    
Group Tu. 16:15-17:45 :   Mi-Song Dupuy   dupuyma.tum.de   MI 03.08.021    

-- MiSongDupuy - 09 Oct 2019