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The mandatory assignment was handed out today. Deadline is Friday May 7, 2010, 15:00.

The lecture on Thursday 29. April is the final one. The dates for oral examination are set to Thursday 3. and Friday 4. of June. The relevant material is taken from the books of Evans (Chapters 3.4 and 11) and Perthame (Chapters 2,3,4,5) + everything covered during lectures.

No lecture tomorrow, Tuesday 13. april, due to sick leave.

Due to me traveling and because of upcoming Easter, the next lecture will be Tuesday April 6. Proceed with self-reading as discussed.

Lecture on Tuesday March 2 is cancelled.

Student representative: Torstein Nilssen [torsteka"@"student.matnat.uio.no].

[Thu Jan 21, Tue Jan 26, Thu Jan 28] Up to now I have been giving an introduction to conservation laws, covering some basic topics like method of characteristics, blow-up of classical solutions, need for weak solutions, Rankine-Hugoniot jump condition, non-uniqueness of weak solutions, need for entropy condition, parabolic conservation laws. Most of this material is covered in Evans' book, cf. Chapter 3.4 (in particular 3.4.1) and Chapter 11 (in particular 11.1.1, 11.4.2, 11.4.3).

The first lecture is on Thursday January 21.

This semester MAT4380 will cover the basic shock wave theory of hyperbolic conservation laws, including mathematical and numerical aspects of the theory. A new feature this semester is that we will emphasize some deep and profound mathematical connections between kinetic theory and conservation laws, as first developed by P.-L. Lions, B. Perthame, and E. Tadmor, and more recently studied and extended by many others. Kinetic equations go back to the nineteenth century and the work of Boltzmann, which unified various perspectives on fluid mechanics. The kinetic equations are characterized by a density function that satisfies a nonlinear conservation law in the phase space. The kinetic approach allows nonlinear conservation laws to be written as linear kinetic (or semi-kinetic) equations acting on nonlinear quantities. Moreover, it will allow us to use the (linear) Fourier transform, regularization and moments methods to provide new approaches for proving uniqueness, reg...