Abstract
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.
Assuming that $\|\om\|_{\L1(\reali)}$ and $\|u_o\|_{\BV(\reali)}$ 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 for which the source term is localized by means of Dirac
masses.
Moreover, we give a characterization of the resulting semigroup
trajectories in
terms of integral estimates.
Anno
2002
Autori IAC
Tipo pubblicazione
Altri Autori
Amadori D., Gosse L., Guerra G.
Editore
Springer.
Rivista
Archive for rational mechanics and analysis (Print)