An example on the limiting case of Sobolev embedding
Sobolev embedding When $p=n$
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Use a reverse method of characteristics to get the trajectories equation
This is an exercise in Evans, Partial Differential Equations (2nd edition), Chapter 10 Conservation laws.
Discontinuous Galerkin method for linear advection equation
PDE This was the first project after I switched to a PhD program in computational math. The goal of the project is to study the Discontinuous Galerkin (DG) f...