We investigate the Cauchy problem for homogeneous equations of order m in the (t, x)-plane, with coefficients depending only on x. Assuming that the characteristic roots satisfy an algebraic condition we succeed in constructing a smooth symmetrizer which behaves like a diagonal matrix: this allows us to prove the well-posedness in C-infinity.
Homogeneous hyperbolic equations with coefficients depending on one space variable
TAGLIALATELA, Giovanni
2007-01-01
Abstract
We investigate the Cauchy problem for homogeneous equations of order m in the (t, x)-plane, with coefficients depending only on x. Assuming that the characteristic roots satisfy an algebraic condition we succeed in constructing a smooth symmetrizer which behaves like a diagonal matrix: this allows us to prove the well-posedness in C-infinity.File in questo prodotto:
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