Boundary behavior of solutions of a class of genuinely nonlinear hyperbolic systems

For a certain class of genuinely nonlinear two-by-two planar hyperbolic systems we show that any classical solution on a smoothly bounded domain has nontangential boundary limits except on a set whose Hausdorff dimension is bounded by some system-dependent constant which is strictly less than 1 and,...

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Veröffentlicht in:arXiv.org 2007-09
1. Verfasser: Gevirtz, Julian
Format: Artikel
Sprache:eng
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Zusammenfassung:For a certain class of genuinely nonlinear two-by-two planar hyperbolic systems we show that any classical solution on a smoothly bounded domain has nontangential boundary limits except on a set whose Hausdorff dimension is bounded by some system-dependent constant which is strictly less than 1 and, on the other hand, that for any system of the kind considered there is in fact a solution on a half-plane which fails to have nontangential limits at a set of boundary points of positive Hausdorff dimension.
ISSN:2331-8422