Nonlocal systems of conservation laws in several space dimensions
| Autor: | Paola Goatin, Rinaldo M. Colombo, Aekta Aggarwal |
|---|---|
| Přispěvatelé: | Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE (OPALE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), INDAM Unit [Roma], Università degli Studi di Brescia [Brescia], Analysis and Control of Unsteady Models for Engineering Sciences (ACUMES), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), European Project: 257661,EC:FP7:ERC,ERC-2010-StG_20091028,TRAM3(2010), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Università degli Studi di Brescia = University of Brescia (UniBs) |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Crowd dynamics
Numerical Analysis Class (set theory) Conservation law Current (mathematics) Applied Mathematics 010102 general mathematics Mathematical analysis Space (mathematics) Nonlocal conservation laws 01 natural sciences 010101 applied mathematics Computational Mathematics Nonlinear system Lax-Friedrichs scheme Convergence (routing) Applied mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Mathematics |
| Zdroj: | SIAM Journal on Numerical Analysis SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2015, 52 (2), pp.963-983 SIAM Journal on Numerical Analysis, 2015, 52 (2), pp.963-983 |
| ISSN: | 0036-1429 |
| Popis: | International audience; We present a Lax-Friedrichs type algorithm to numerically integrate a class of nonlocal and nonlinear systems of conservation laws in several space dimensions. The convergence of the approximate solutions is proved, also providing the existence of solution in a slightly more general setting than in other results in the current literature. An application to a crowd dynamics model is considered. This numerical algorithm is then used to test the conjecture that as the convolution kernels converge to a Dirac $\delta$, the nonlocal problem converges to its non-nonlocal analogue. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|