Preprint 2004-010

Well-Posedness fo a Scalar Conservation Law with Singular Non-Conservative Source

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

a_t=0,    u_t+f(a,u)_x - g(a,u)a_x =0      (a,u)(0,\cdot)=(a_o,u_o).

For possibly large, discontinuous data, the continuous dependence of the solution with respect to both $a_o$ and $u_o$ is shown. Moreover the solutions are characterized as unique limits of Kru\v zkov's entropic solutions constructed with regularized initial data $a^\varepsilon_o$.

Paper:

Available as Postscript (504 Kbytes) or gzipped PostScript (184 Kbytes; uncompress using gunzip).

Author(s):

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

Publishing information:

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Submitted by:

<graziano.guerra@unimib.it> March 19 2004.