UMD PDE Qualifying Exams/Jan2011PDE

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Problem 1[edit]

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[edit]