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- W2005097390 abstract "We introduce the concept of modular family of entropy vectors for general r x r systems of balance laws. We then define the notion of entropy solution to the Cauchy problem compatible with the modular family, assuming that the system admits such a family. We show that this concept reduces to the usual one, introduced by S.N. Kruzkov, in the scalar case and when we restrict ourself to Lipschitz continuous solutions. We also show how the compatibility condition appears in the cases of symmetric systems, 2 x 2 psystems and equations of hyperelasticity and electromagnetism, the last two considered earlier by C.M. Dafermos. We demonstrate that generalized Oleinik's condition implies our compatibility condition in the case of symmetric systems. We prove the uniqueness and stability relatively to the initial data of the entropy solutions compatible with the modular family. This theorem has as corollary uniqueness results due to O.A. Oleinik, S.N. Kruzkov, A.E. Hurd, R.J. DiPerna and C. Bardos. We give also two u..." @default.
- W2005097390 created "2016-06-24" @default.
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- W2005097390 date "1989-01-01" @default.
- W2005097390 modified "2023-09-26" @default.
- W2005097390 title "Uniqueness of Solutions to Hyperbolic Balance Laws in Several Space Dimensions" @default.
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- W2005097390 doi "https://doi.org/10.1080/03605308908820638" @default.
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