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dc.contributor.author
Christodoulou, Demetrios
dc.contributor.author
Pérez, Daniel R.
dc.date.accessioned
2017-06-12T00:06:49Z
dc.date.available
2017-06-12T00:06:49Z
dc.date.issued
2015
dc.identifier.uri
http://hdl.handle.net/20.500.11850/112365
dc.description.abstract
An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in two variables has a global C2-solution for small enough initial data. Inspired by recent work of D. Christodoulou, we revisit John's original proof and extract a more precise description of the behaviour of solutions at the time of shock. We show that John's singular first order quantity, when expressed in characteristic coordinates, remains bounded until the final time, which is then characterised by an inverse density of characteristics tending to zero in one point. Moreover, we study the derivatives of second order, showing again their boundedness when expressed in appropriate coordinates. We also recover John's upper bound for the time of shock formation and complement it with a lower bound. Finally, we apply these results to electromagnetic plane waves in a crystal with no magnetic properties and cubic electric non-linearity in the energy density, assuming no dispersion.
dc.language.iso
en
dc.publisher
Cornell University
dc.title
On the formation of shocks of electromagnetic plane waves in non-linear
dc.type
Working Paper
ethz.journal.title
arXiv
ethz.pages.start
arXiv1505.04101
ethz.notes
See also: http://e-citations.ethbib.ethz.ch/view/pub:181686.
ethz.publication.place
Ithaca, NY
ethz.publication.status
published
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03583 - Christodoulou, Demetrios (emeritus)
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03583 - Christodoulou, Demetrios (emeritus)
ethz.identifier.url
http://arxiv.org/abs/1505.04101v1
ethz.date.deposited
2017-06-12T00:10:41Z
ethz.source
ECIT
ethz.identifier.importid
imp5936541346f7598387
ethz.ecitpid
pub:173901
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-12T16:57:29Z
ethz.rosetta.lastUpdated
2018-11-02T22:15:08Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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