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Well-posedness of hyperbolic system with constant coefficients in finite domains

I'm studying the PDE $$ \frac{\partial u}{\partial t} + A_x\frac{\partial u}{\partial x} + A_y\frac{\partial u}{\partial y} + A_z\frac{\partial u}{\partial z} = 0 $$ with $A_x, A_y, A_z$ being con …
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