Global BV Entropy Solutions and Uniqueness for Hyperbolic Systems of Balance Laws

2002 ◽  
Vol 162 (4) ◽  
pp. 327-366 ◽  
Author(s):  
Debora Amadori ◽  
Laurent Gosse ◽  
Graziano Guerra
Keyword(s):  
Hyperbolic Systems ◽  
Entropy Solutions ◽  
Balance Laws ◽  
Systems Of Balance Laws

scholarly journals On the structure of BV entropy solutions for hyperbolic systems of balance laws with general flux function

2019 ◽  
Vol 16 (02) ◽  
pp. 333-378
Author(s):  
Fabio Ancona ◽  
Laura Caravenna ◽  
Andrea Marson
Keyword(s):  
Conservation Laws ◽  
Wave Front ◽  
Hyperbolic System ◽  
Hyperbolic Conservation Laws ◽  
Hyperbolic Systems ◽  
Entropy Solutions ◽  
Balance Laws ◽  
Hyperbolic Conservation ◽  
Flux Function ◽  
Systems Of Balance Laws

The paper describes the qualitative structure of BV entropy solutions of a general strictly hyperbolic system of balance laws with characteristic field either piecewise genuinely nonlinear or linearly degenerate. In particular, we provide an accurate description of the local and global wave-front structure of a BV solution generated by a fractional step scheme combined with a wave-front tracking algorithm. This extends the corresponding results in [S. Bianchini and L. Yu, Global structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one space dimension, Comm. Partial Differential Equations 39(2) (2014) 244–273] for strictly hyperbolic system of conservation laws.

ONE-SIDED ESTIMATES AND UNIQUENESS FOR HYPERBOLIC SYSTEMS OF BALANCE LAWS

2003 ◽  
Vol 13 (04) ◽  
pp. 527-543 ◽  
Author(s):  
PAOLA GOATIN
Keyword(s):  
Hyperbolic Systems ◽  
Decay Estimates ◽  
Balance Laws ◽  
Uniqueness Of Solutions ◽  
Local Oscillation ◽  
Systems Of Balance Laws

Uniqueness of solutions of genuinely nonlinear n × n strictly hyperbolic systems of balance laws is established moving from Oleïnik-type decay estimates. As middle step, the result relies on the fulfillment of a condition which controls the local oscillation of the solution in a forward neighborhood of each point in the t–x plane.

scholarly journals A remark on the Glimm scheme for inhomogeneous hyperbolic systems of balance laws

2015 ◽  
Vol 12 (04) ◽  
pp. 787-797 ◽  
Author(s):  
Cleopatra Christoforou
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Weak Solutions ◽  
State Vector ◽  
Equilibrium Solution ◽  
Hyperbolic Systems ◽  
Balance Laws ◽  
Glimm Scheme ◽  
Systems Of Balance Laws ◽  
The Cauchy Problem

General hyperbolic systems of balance laws with inhomogeneous flux and source are studied. Global existence of entropy weak solutions to the Cauchy problem is established for small BV data under appropriate assumptions on the decay of the flux and the source with respect to space and time. There is neither a hypothesis about equilibrium solution nor about the dependence of the source on the state vector as previous results have assumed.

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