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Admissible BV solutions to the Cauchy problem for general strictly hyperbolic systems of conservation laws, under initial data with small total variation, will be constructed by the vanishing viscosity method. These solutions are unique and may be realized as orbits of the L1-Lipschitz continuous Viscosity Semigroup which parallels the Standard Riemann Semigroup, introduced in Chapter XIV.

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Construction of BV Solutions by the Vanishing Viscosity Method and the Issue of Uniqueness

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  • 发表日期：

    2026年

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  • Constantine M. Dafermos

摘要

Admissible BV solutions to the Cauchy problem for general strictly hyperbolic systems of conservation laws, under initial data with small total variation, will be constructed by the vanishing viscosity method. These solutions are unique and may be realized as orbits of the L1-Lipschitz continuous Viscosity Semigroup which parallels the Standard Riemann Semigroup, introduced in Chapter XIV.