Preprint 2000-050

Global BV Entropy Solutions and Uniqueness for Hyperbolic Systems of Balance Laws

Debora Amadori, Laurent Gosse, and Graziano Guerra

Abstract: We consider the Cauchy problem for $n\times n$ strictly hyperbolic systems of balance laws
    u_t+f(u)_x=g(x,u),  x \in R, t>0\\
    u(0,.)=u_0 \in L^1 \cap {\bf BV}(R; R^n), \\
    |\lambda_i(u)| \geq c > 0 for all  i\in \{1,\ldots,n\}, \\
    |g(.,u)|+|\nabla_u g(.,u)|\leq \omega \in L^1\cap L^\infty(R),
each characteristic field being genuinely nonlinear or linearly degenerate. Assuming that $\|\omega\|_{L^1(R)}$ and $\|u_o\|_{{\bf BV}(R)}$ are small enough, we prove the existence and uniqueness of global entropy solutions of bounded total variation as limits of special wave-front tracking approximations. Moreover, we give a characterization of the semigroup trajectories in terms of integral estimates.

Available as PostScript (485 Kbytes) or gzipped PostScript (182 Kbytes; uncompress using gunzip).
Debora Amadori, <>
Laurent Gosse, <>
Graziano Guerra, <>
Publishing information:
Submitted by:
<> December 11 2000.

[ 1996 | 1997 | 1998 | 1999 | 2000 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
Last modified: Tue Dec 12 14:03:22 MET 2000