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UMD PDE Qualifying Exams/Jan2011PDE
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Problem 1
Consider the conservation law
where .
(a) Define an integral solution of the PDE
(b) Derive the jump (Rankine-Hugoniot) condition satisfied by a piecewise smooth integral solution across a curve where this has a discontinuity.
(c) Find an integral solution to the PDE when with if if .
Solution