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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
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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 …