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Well‐posedness of IBVP for 1D scalar non‐local conservation laws
Author(s) -
Goatin Paola,
Rossi Elena
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800318
Subject(s) - conservation law , uniqueness , scalar (mathematics) , mathematics , lipschitz continuity , boundary value problem , mathematical analysis , operator (biology) , dimension (graph theory) , pure mathematics , geometry , biochemistry , chemistry , repressor , transcription factor , gene
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.