Methods and Applications of Analysis

Volume 20 (2013)

Number 1

Weakly well posed hyperbolic initial-boundary value problems with non characteristic boundary

Pages: 1 – 32

DOI: http://dx.doi.org/10.4310/MAA.2013.v20.n1.a1

Authors

Alessandro Morando (DICATAM, Sezione di Matematica, Università di Brescia, Italy)

Paola Trebeschi (DICATAM, Sezione di Matematica, Università di Brescia, Italy)

Abstract

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.

Keywords

symmetrizable systems, symmetric hyperbolic systems, mixed initial-boundary value problem, weak well posedness, loss of derivatives, Sobolev spaces

2010 Mathematics Subject Classification

35L40, 35L50

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