18.306 Lecture 14 - Tue 2021 04 13 - Virtual
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Example:  "Shock structure"
Shock as a traveling wave for  u_t + Q(u)_x = (nu*u_x),  nu = nu(u) > 0.
Q convex or concave.
Show it satisfies Rankine-Hugoniot and entropy.
Show it gives shock in limit nu \to 0

Example: Show "energy" decreases
         for u_t + Q(u)_x = (nu*u_x),  nu = nu(u) > 0.
Show that, for traveling wave, energy loss is independent of nu \to 0.
Compute energy loss for shock solution of u_t + Q(u)_x = 0.

#031  SKIP, but make connection with last point [u^2 is dissipated by shock].
#032a SKIP
#032b Source term does not affect shock conditions.
#033a Weak derivatives and weak solutions.

Examples to do:
u_t + (0.5*u^2)_x = -a*u with triangle initial condition.
u_t + (0.5*u^2)_x = 0    Formation of S and N waves from compact data.
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