Differential and Integral Equations

The semigroup generated by a Temple class system with non-convex flux function

Stefano Bianchini

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Abstract

We consider the Cauchy problem for a nonlinear $n \times n$ system of conservation laws of Temple class, i.e., with coinciding shock and rarefaction curves and with a coordinate system made of Riemann invariants. Without any assumption on the convexity of the flux function, we prove the existence of a semigroup made of weak solutions of the equations and depending Lipschitz continuously on the initial data with bounded total variation.

Article information

Source
Differential Integral Equations Volume 13, Number 10-12 (2000), 1529-1550.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061138

Mathematical Reviews number (MathSciNet)
MR1787080

Zentralblatt MATH identifier
1043.35110

Subjects
Primary: 35L65: Conservation laws
Secondary: 35D05 35L67: Shocks and singularities [See also 58Kxx, 76L05] 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]

Citation

Bianchini, Stefano. The semigroup generated by a Temple class system with non-convex flux function. Differential Integral Equations 13 (2000), no. 10-12, 1529--1550. https://projecteuclid.org/euclid.die/1356061138.


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