| Abstract: |
| 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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