UMD PDE Qualifying Exams/Jan2011PDE

Problem 1Edit

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  .

SolutionEdit