Global BV entropy solutions and uniqueness for hyperbolic systems of balance laws
We consider the Cauchy problem for $n\times n$ strictly hyperbolic
systems of
nonresonant balance laws
$$
\left\{\begin{array}{c}
u_t+f(u)_x=g(x,u), \qquad x \in \reali, t>0\\
u(0,.)=u_o \in \L1 \cap \BV(\reali; \reali^n), \\
| \la_i(u)| \geq c > 0 \mbox{ for all } i\in \{1,\ldots,n\}, \\
|g(.,u)|+\norma{\nabla_u g(.,u)}\leq \om \in \L1\cap\L\infty(\reali), \\
\end{array}\right.
$$
each characteristic field being genuinely nonlinear or linearly
degenerate.






