We model the flow of a fluid in a pipe by a first-order nonlinear hyperbolic system with zero-order nonlinear dissipation. We prove that a unique, global smooth solution exists if the initial data are in an appropriate invariant region and if the first derivatives of the initial data are sufficiently small.
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* Supported by AFOSR under Contract F49620-79-C-0149 at the &ole Polytechnique Fed&ale, Lausanne. Switzerland.