Oleinik Type Estimates and Uniqueness for n x n Conservation Laws
A. Bressan and P. Goatin
Let $u_t + f(x)_x =0$ be a strictly hyperbolic $n\times n$
system of conservation laws in one space dimension. Relying
on the existence of a semigroup of solutions, we first establish
the uniqueness of entropy admissible weak solutions to the
Cauchy problem, under a mild assumption on the local oscillation
of $u$ in a forward neighborhood of each point in the $t-x$
plane. In turn, this yields the uniqueness of weak solutions
which satisfy a decay estimate on positive waves of genuinely
nonlinear families, thus extending a classical result proved
by Oleinik in the scalar case.
- Available as PostScript
- Oleinik type estimates and uniqueness for n x n conservation laws
- A. Bressan,
- P. Goatin,
- Publishing information:
- To appear in J. Diff. Eq.
- Revised version, October 11 1998.
- Submitted by:
December 11 1997.
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