Blowup in L∞ for a class of genuinely nonlinear hyperbolic systems of conservation laws

Paolo Baiti; Helge Kristian Jenssen

Blowup in L^∞ for a class of genuinely nonlinear hyperbolic systems of conservation laws

Paolo Baiti
, Helge Kristian Jenssen

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a class of 3 × 3 systems of conservation laws with all characteristic fields genuinely nonlinear, and we show the existence of entropy solutions for these that blow up in sup-norm in finite time. The solutions are constructed by considering wave patterns where infinitely many shock waves are produced in finite time. We also consider the role of entropies as a mechanism for preventing this type of singular behavior.

Original language	English (US)
Pages (from-to)	837-853
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems
Volume	7
Issue number	4
State	Published - Dec 1 2001

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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abstract = "We construct a class of 3 × 3 systems of conservation laws with all characteristic fields genuinely nonlinear, and we show the existence of entropy solutions for these that blow up in sup-norm in finite time. The solutions are constructed by considering wave patterns where infinitely many shock waves are produced in finite time. We also consider the role of entropies as a mechanism for preventing this type of singular behavior.",

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AU - Jenssen, Helge Kristian

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N2 - We construct a class of 3 × 3 systems of conservation laws with all characteristic fields genuinely nonlinear, and we show the existence of entropy solutions for these that blow up in sup-norm in finite time. The solutions are constructed by considering wave patterns where infinitely many shock waves are produced in finite time. We also consider the role of entropies as a mechanism for preventing this type of singular behavior.

AB - We construct a class of 3 × 3 systems of conservation laws with all characteristic fields genuinely nonlinear, and we show the existence of entropy solutions for these that blow up in sup-norm in finite time. The solutions are constructed by considering wave patterns where infinitely many shock waves are produced in finite time. We also consider the role of entropies as a mechanism for preventing this type of singular behavior.

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M3 - Article

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SN - 1078-0947

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JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 4

ER -

Blowup in L^∞ for a class of genuinely nonlinear hyperbolic systems of conservation laws

Abstract

All Science Journal Classification (ASJC) codes

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