Abstract
We consider different situations of blowup in sup-norm for hyperbolic equations. For scalar conservation laws with a source the asymptotic profile of the solution close to a blowup point is described in detail. Based on an example of Jeffrey we next show how blowup for ordinary differential equations can be used to construct examples of blowup for systems of hyperbolic equations. Finally we outline the construction of solutions to certain strictly hyperbolic 3 x 3-systems of conservation laws which blow up in either sup-norm or total variation norm in finite time.
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Jenssen, H.K., Sinestrari, C. (1999). Blowup for Hyperbolic Equations. In: Jeltsch, R., Fey, M. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8724-3_2
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DOI: https://doi.org/10.1007/978-3-0348-8724-3_2
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