Methods and Applications of Analysis
Volume 20 (2013)
Weakly well posed hyperbolic initial-boundary value problems with non characteristic boundary
Pages: 1 – 32
We study the mixed initial-boundary value problem for a linear hyperbolic system with non characteristic boundary. We assume the problem to be “weakly” well posed, in the sense that a unique $L^2$-solution exists, for sufficiently smooth data, and obeys an a priori energy estimate with a finite loss of regularity. This is the case of problems that do not satisfy the uniform Kreiss-Lopatinskiǐ condition. Under the assumption of the loss of one tangential derivative, we obtain the Sobolev regularity of solutions, provided the data are sufficiently smooth.
symmetrizable systems, symmetric hyperbolic systems, mixed initial-boundary value problem, weak well posedness, loss of derivatives, Sobolev spaces
2010 Mathematics Subject Classification