We consider the Cauchy problem for n × n strictly hyperbolic systems of non-resonant balance laws, each characteristic field being genuinely nonlinear or linearly degenerate. Assum- ing that ∥ω∥L1(R) and ∥uo∥BV(R) are small enough, we prove the existence and uniqueness of global entropy solutions of bounded total variation as limits of spe- cial wave-front tracking approximations for which the source term is localized by means of Dirac masses. Moreover, we give a characterization of the resulting semigroup trajectories in terms of integral estimates.

Global BV entropy solutions and uniqueness for hyperbolic systems of balance laws

AMADORI, DEBORA;
2002

Abstract

We consider the Cauchy problem for n × n strictly hyperbolic systems of non-resonant balance laws, each characteristic field being genuinely nonlinear or linearly degenerate. Assum- ing that ∥ω∥L1(R) and ∥uo∥BV(R) are small enough, we prove the existence and uniqueness of global entropy solutions of bounded total variation as limits of spe- cial wave-front tracking approximations for which the source term is localized by means of Dirac masses. Moreover, we give a characterization of the resulting semigroup trajectories in terms of integral estimates.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/20501
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