On the initial boundary value problem for Temple systems

DOI10.1016/j.na.2003.09.022zbMath1058.35150OpenAlexW2042225820MaRDI QIDQ1879178

Alessandro Groli, Rinaldo M. Colombo

Publication date: 22 September 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2003.09.022

zbMATH Keywords

conservation lawsglobal existenceinitial boundary value problemweak entropy solution is established. Stability in the \(L^1\)-norm

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Initial-boundary value problems for first-order hyperbolic systems (35L50)

Related Items (7)

Wave front tracking in systems of conservation laws. ⋮ Global well posedness of traffic flow models with phase transitions ⋮ The initial boundary value problem for second order traffic flow models with vacuum: existence of entropy weak solutions ⋮ Existence of nonclassical solutions in a pedestrian flow model ⋮ Well posedness of balance laws with boundary ⋮ Data-driven uncertainty quantification in macroscopic traffic flow models ⋮ A mixed ODE–PDE model for vehicular traffic

Cites Work

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• The semigroup generated by a Temple class system with large data
• A \(2\times 2\) hyperbolic traffic flow model
• Minimising stop and go waves to optimise traffic flow.
• The semigroup generated by \(2 \times 2\) conservation laws
• On the Attainable Set for Scalar Nonlinear Conservation Laws with Boundary Control
• Hyperbolic Phase Transitions in Traffic Flow
• Uniqueness and Stability of $ L^\infty$ Solutions for Temple Class Systems with Boundary and Properties of the Attainable Sets
• Resurrection of "Second Order" Models of Traffic Flow
• Systems of Conservation Laws with Invariant Submanifolds
• The semigroup generated by a Temple class system with non-convex flux function.

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