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Communication Dans Un Congrès Année : 2023

A non-conservative and non-strictly hyperbolic diagonal system related to crystallography

Stéphane Junca
Maryam Al Zohbi
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  • IdRef : 263813878

Résumé

A $ d \times d $ non-conservative and non strictly hyperbolic but hyperbolic diagonal system appearing in the theory of dislocations is studied in the framework of fractional $BV$ spaces. A definition of entropy solution is proposed for this non-conservative system. Existence of entropy solutions in $BV^s$ for all $ 0 2$. The infinite family of entropies for $d=2$ is not enough to ensure uniqueness due to the loss of stric hyperbolicity. Entropy Riemann solvers that recover main properties of vanishing viscosity solutions exhibit more waves than usual, already for $d=2$.
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Dates et versions

hal-04197314 , version 1 (06-09-2023)

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  • HAL Id : hal-04197314 , version 1

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Stéphane Junca, Maryam Al Zohbi. A non-conservative and non-strictly hyperbolic diagonal system related to crystallography. 13th AIMS Conference on Dynamical Systems, Differential equations and Applications, May 2023, Wilmington, United States. ⟨hal-04197314⟩
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