DECAY OF POSITIVE WAVES OF HYPERBOLIC BALANCE LAWS

doi:10.1016/S0252-9602(12)60022-8

Abstract

Abstract:

Historically, decay rates have been used to provide quantitative and quali-tative information on the solutions to hyperbolic conservation laws. Quantitative results include the establishment of convergence rates for approximating procedures and numer-ical schemes. Qualitative results include the establishment of results on uniqueness and regularity as well as the ability to visualize the waves and their evolution in time. This work presents two decay estimates on the positive waves for systems of hyperbolic and gen-uinely nonlinear balance laws satisfying a dissipative mechanism. The result is obtained by employing the continuity of Glimm-type functionals and the method of generalized characteristics [7, 17, 24].

Key words: hyperbolic conservation law, total variation, interaction potential, Glimm functional, spreading of rarefaction wave, piecewise genuinely nonlinear, nonclassical solution

CLC Number:

35l65

Cleopatra Christoforou, Konstantina Trivisa. DECAY OF POSITIVE WAVES OF HYPERBOLIC BALANCE LAWS[J].Acta mathematica scientia,Series B, 2012, 32(1): 352-366.

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