Preprint 1996-043

Decay of Positive Waves in Nonlinear Systems of Conservation Laws

Abstract: This paper is concerned with BV solutions to a system of conservation laws in one space dimension:
$$
u_t+ \left[ f(u) \right]_x = 0
$$
Here $t \in [0,T]$ and $f \colon \Omega \mapsto {\bf R}^n$ is smooth, with $\Omega \subseteq {\bf R}^n$. We assume that the system is strictly hyperbolic, and that each characteristic field is either linearly degenerate or genuinely nonlinear. Our aim is to derive a priori bounds on the strength of positive waves of genuinely nonlinear families, which extend the classical decay estimates of Oleinik.

Paper:

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Title: Decay of Positive Waves in Nonlinear Systems of Conservation Laws

Author(s):

Alberto Bressan mailto:bressan@sissa.it

Rinaldo M. Colombo mailto:rinaldo@imiucca.csi.unimi.it

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Submitted by:

mailto:rinaldo@vmimat.mat.unimi.it December 9 1996.