Abstract
where u= u(t; x) is the state variable, u; ũ are integrable (possibly unbounded) initial and boundary data, and f is assumed to be a superlinear strictly convex function. For problems of this type, since classical solutions develop discontinuities in nite time, no matter how smooth their initial and boundary data, it is natural to consider weak solutions satisfying the usual entropy conditions ([13, 15]) u(t; x−)≥ u(t; x+); t; x?0: (1.4)
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