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NONCONVEX CONSERVATION LAWS AND ORDINARY DIFFERENTIAL EQUATIONS
Published online by Cambridge University Press: 29 March 2004
Abstract
The paper deals with the well posedness of a class of ordinary differential equations. The vector field depends on the solution to a scalar conservation law, whose flux function is assumed to have a single inflection point (from whence ‘nonconvex’ is derived). Filippov solutions to the ordinary differential equations are considered, and Hölder continuous dependence on the initial data is proved. The motivation for the problem is a model of traffic flow.
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- The London Mathematical Society 2004
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