We present recent results about the mixed initial-boundary value problem for a linear hyperbolic system with characteristic boundary of constant multiplicity. We assume the problem to be ''weakly'' well posed, namely that a unique L^2-solution exists, for sufficiently smooth data, and obeys an a priori energy estimate with a finite loss of conormal regularity. Under the assumption of the loss of one conormal derivative, we obtain the regularity of solutions in the natural framework of the anisotropic Sobolev spaces, provided the data are sufficiently smooth.
Weakly well posed characteristic hyperbolic problems
MORANDO, Alessandro;SECCHI, Paolo
2012-01-01
Abstract
We present recent results about the mixed initial-boundary value problem for a linear hyperbolic system with characteristic boundary of constant multiplicity. We assume the problem to be ''weakly'' well posed, namely that a unique L^2-solution exists, for sufficiently smooth data, and obeys an a priori energy estimate with a finite loss of conormal regularity. Under the assumption of the loss of one conormal derivative, we obtain the regularity of solutions in the natural framework of the anisotropic Sobolev spaces, provided the data are sufficiently smooth.File in questo prodotto:
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