Quasilinear first order equations. Linear elliptic, parabolic, and hyperbolic equations of second order. Methods: maximum principle, Sobolev spaces, variational principles, spectral analysis
Lectures, exercies and a revision course are being offered. In the lecture there will be an introduction to theory and examples will be calculated. Once a week, exercise-sheets will be calculated on the blackboard by the students.The repetition offers the possibliy to make questions relating the lecture. The repetition is a complementary and optional offer.
Lecture Notes available on the website: http://www.asc.tuwien.ac.at/~juengel->Teaching (latest version: March 2022)
* for the individual chapters of the course:
§1: Strauss §1.1-1.5; Evans §2.1
§2: Evans §3.2; Strauss §1.6, (14.1)
§3: Renardy-Rogers §5.1-5.3; Strauss §12.1
§4: Evans §2.2; Strauss §6.1-6.3, 7.3, 12.2
§5: Evans §5+6
§6: Straus §12.3, 2.4, 4.1; Evans §2.3.1, 2.3.3, 4.3.1, D.6, (7.1)
§7: Straus §2.1-2.2, 2.5, 3.2, 4.1, 9.1; Evans §2.4.1a, 2.4.3, 7.2
* general:
W.A. Strauss: Partial Differential Equations - An Introduction, John Wiley & Sons, 1992
L.C. Evans: Partial Differential Equations, AMS, 1998
F. John, Partial Differential Equations, Springer, New York, 1975.
M. Renardy, R.C. Rogers, An Introduction to Partial Differential Equations, Springer, New York, 1993
M.E. Taylor, Partial Differential Equations - Basic Theory, Springer, 1996
* analysis 1-3
* differential equations 1 (solving equations of 1st and 2nd order with constant coefficients [also inhomogeneous], variation of constants, separation of variables)
* functional analysis (in particular compactness, strong/weak convergence, L^p spaces, Hilbert spaces, dual spaces, Riesz-Fischer representation theorem, linear operators, spectrum)
It is recommended to take the exams for the above mentioned lectures before attending the lecture Partial Differential equations.
