Alessandro Morando and Paolo Secchi
Weakly well posed characteristic hyperbolic problems
Received: 30 September 2010
Accepted: 13 December 2010
Mathematics Subject Classification (2000): 35L40, 35L50.
Keywords: Symmetric and symmetrizable hyperbolic systems, initial-boundary value problem, weak well posedness, characteristic boundary, anisotropic Sobolev spaces, tangential regularity.
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 L2-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.