Lecture 05, 18.376, Thu Feb 23, 2023.
Summary
%
Lecture given by Kyle McGee.
Discussed the basics of the method of characteristics, demonstrating by a
simple example. Then, qualitatively, gave an explanation for how
1) multivaluedness (potentially shocks) and
2) regions of no solution can emerge.
Through examples, showed one method of resolving multivaluedness,
using shocks. Derived the Rankine--Hugoniot conditions using conservation
and stated the LAX entropy condition. Also mentioned that shocks imply
narrow region of dissipation, so one should look at the physics to ensure
this is an appropriate model (Sketched the calculation which shows that
the original conservation law does not imply a higher conservation law
(e.g.: energy) when shocks are present). Also showed how expansion fans
can resolve issue #2.
%
% ==========================================================================
NOTE: Here #nnn	are references to the Lecture Points file.
      [PSQ] means Problem Set Question.
 The "lecture summaries and points" are NOT intended as study materials.
 The points purpose is explained in the "lecture points" file.
 The summaries are brief descriptions each lecture, used by the instructor
 to keep track of the material covered. They ARE *NOT* "lecture notes" to
 be used to study and/or replace attending the lectures, etc. They are
 provided for your convenience, as a help to organize your own notes.
% ==========================================================================
% EOF