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

Julian Gevirtz

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

Julian Gevirtz

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Abstract

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.

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Julian Gevirtz. 2007-09-16. Boundary behavior of solutions of a class of genuinely nonlinear hyperbolic systems. https://arxiv.org/abs/math/0703294

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