We are concerned with global, weak solutions to the Cauchy problem for a (strictly hyperbolic) system of balance laws \begin{displaymath}\left\{\begin{array}{l}u_t + [F(u)]_x = g(u)\\u(0,x) = u_0(x).\end{array} \right.\end{displaymath} Assume that the initial data has small total variation. We give a sufficient condition for global existence of solutions in $\mathinner{\bf BV}$. Such condition generalizes the one required by Dafermos and Hsiao in a paper of them (1982).
Amadori, D., Guerra, G. (1999). Global weak solutions for systems of balance laws. APPLIED MATHEMATICS LETTERS, 12(6), 123-127 [10.1016/S0893-9659(99)00090-7].
Global weak solutions for systems of balance laws
GUERRA, GRAZIANO
1999
Abstract
We are concerned with global, weak solutions to the Cauchy problem for a (strictly hyperbolic) system of balance laws \begin{displaymath}\left\{\begin{array}{l}u_t + [F(u)]_x = g(u)\\u(0,x) = u_0(x).\end{array} \right.\end{displaymath} Assume that the initial data has small total variation. We give a sufficient condition for global existence of solutions in $\mathinner{\bf BV}$. Such condition generalizes the one required by Dafermos and Hsiao in a paper of them (1982).
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