We consider the initial boundary value problem (IBVP) for a non‐local scalar conservation law in one space dimension. The non‐local operator in the flux function is not a mere convolution product, but it is assumed to be aware of boundaries. Introducing an adapted Lax‐Friedrichs algorithm, we provide various estimates on the approximate solutions that allow to prove the existence of solutions to the original IBVP. The uniqueness follows from the Lipschitz continuous dependence on initial and boundary data, which is proved exploiting results available for the local IBVP
Well‐posedness of IBVP for 1D scalar non‐local conservation laws / Goatin, P; Rossi, E. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK. - ISSN 0044-2267. - 99:11(2019). [10.1002/zamm.201800318]
Well‐posedness of IBVP for 1D scalar non‐local conservation laws
Rossi, E
2019
Abstract
We consider the initial boundary value problem (IBVP) for a non‐local scalar conservation law in one space dimension. The non‐local operator in the flux function is not a mere convolution product, but it is assumed to be aware of boundaries. Introducing an adapted Lax‐Friedrichs algorithm, we provide various estimates on the approximate solutions that allow to prove the existence of solutions to the original IBVP. The uniqueness follows from the Lipschitz continuous dependence on initial and boundary data, which is proved exploiting results available for the local IBVP
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