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Volume 1,     Number 4,     Fall 1993

 

A MODEL EQUATION FOR
SHOCK WAVES IN RANDOM MEDIA
JOHN K. HUNTER AND R. VEDANTHAM

Abstract. The propagation of weakly nonlinear high frequency hyperbolic waves through a random medium is described by an inviscid Burgers' equation with random time dependent coefficients. This Burgers' equation provides an exactly solvable model equation for shocks in a random media. We derive an effective equation for the mean of stochastically time shifted solutions, and we study the statistics of the shock formation time.

 

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