This 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 (whence ``nonconvex''). We consider Filippov solutions to the o.d.e. and prove H\"older continuous dependence on the initial data. The problem is motivated by a model of traffic flow.
Nonconvex conservation laws and Ordinary Differential Equations
MARSON, ANDREA
2004
Abstract
This 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 (whence ``nonconvex''). We consider Filippov solutions to the o.d.e. and prove H\"older continuous dependence on the initial data. The problem is motivated by a model of traffic flow.
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