Summary: The paper deals with the initial-boundary value problem for a 1-D scalar conservation law in the case of $L^1$ initial and boundary data. The generalized solutions are constructed via semigroup theory, and a comparison principle as well as explicit (variational) representations for the solutions are obtained. Also the attainable set as $t=T$ is described for integrable boundary data considered as control. These results are applied to the concrete problem of optimal traffic flo
Scalar non-linear conservation laws with integrable boundary data
ANCONA, FABIO;MARSON, ANDREA
1999
Abstract
Summary: The paper deals with the initial-boundary value problem for a 1-D scalar conservation law in the case of $L^1$ initial and boundary data. The generalized solutions are constructed via semigroup theory, and a comparison principle as well as explicit (variational) representations for the solutions are obtained. Also the attainable set as $t=T$ is described for integrable boundary data considered as control. These results are applied to the concrete problem of optimal traffic flo
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