Abstract
In this chapter we introduce the definitions of boundary data and of constraints. More precisely, we study the initial-boundary value problem in Sect. 6.2, the constrained Riemann problem in Sect. 6.3, the constrained Cauchy problem in Sect. 6.4 and finally the constrained initial-boundary value problem in the last section.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andreianov, B., Goatin, P., Seguin, N.: Finite volume schemes for locally constrained conservation laws. Numerische Mathematik 115, 609–645 (2010)
Bardos, C., le Roux, A.Y., Nédélec, J.C.: First order quasilinear equations with boundary conditions. Comm. Partial Differential Equations 4(9), 1017–1034 (1979)
Colombo, R.M., Goatin, P.: A well posed conservation law with a variable unilateral constraint. J. Differential Equations 234(2), 654–675 (2007)
Colombo, R.M., Goatin, P., Rosini, M.D.: Conservation laws with unilateral constraints in traffic modeling. In: Mussone, L., Crisalli, U. (eds.) Transport Management and Land-Use Effects in Presence of Unusual Demand, Atti del Convegno SIDT 2009 (June 2009)
Kružhkov, S.N.: First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81(123), 228–255 (1970)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 SpringerBerlin Heidelberg
About this chapter
Cite this chapter
Rosini, M.D. (2013). The Initial-Boundary Value Problem and the Constraint. In: Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications. Understanding Complex Systems. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00155-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-00155-5_6
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00154-8
Online ISBN: 978-3-319-00155-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)