Preprint 2003-015

Godunov-Type Approximation for a General Resonant Balance Law with Large Data

Abstract: We consider the Cauchy problem for the $2\times 2$ nonstrictly hyperbolic system

at=0,		(a,u)(0,\cdot)=(ao,uo).
ut+f(a,u)x - g(a,u)ax =0,

For possibly large, discontinuous and resonant data, the generalized solution to the Riemann problem is introduced, interaction estimates are carried out using a new change of variables and the convergence of Godunov approximations is shown. Uniqueness is addressed relying on a suitable extension of Kru\v zkov's techniques.

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Author(s):

Debora Amadori, <amadori@univaq.it>

Laurent Gosse, <l.gosse@area.ba.cnr.it>

Graziano Guerra, <graziano.guerra@unimib.it>

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<graziano.guerra@unimib.it> February 17 2003.