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A new proof of indefinite propagation of singularities for a Hamilton-Jacobi equation
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Number of Authors: 12016 (English)In: Journal of evolution equations (Printed ed.), ISSN 1424-3199, E-ISSN 1424-3202, Vol. 16, no 4, p. 895-903Article in journal (Refereed) Published
Abstract [en]

We study propagation of singularities for the Hamilton–Jacobi equation S t +H(∇S)=0,(t,x)∈(0,T)×R n , St+H(∇S)=0,(t,x)∈(0,T)×Rn,where H(p)=12 ⟨p,Ap⟩ H(p)=12⟨p,Ap⟩ is a positive definite quadratic form. Each viscosity solution S S is semiconcave, and it is known that its singularities move along generalized characteristics. We give a new proof of the recent result by Cannarsa et al. (Discrete Contin Dyn Syst 35:4225–4239, 2015), namely that the singularities propagate along generalized characteristics indefinitely forward in time. 

Place, publisher, year, edition, pages
2016. Vol. 16, no 4, p. 895-903
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-6048DOI: 10.1007/s00028-016-0324-8ISI: 000389353300006Scopus ID: 2-s2.0-84959375483Local ID: 43dc79c1-711d-46d9-99b8-84a9dcb9e3d9OAI: oai:DiVA.org:ltu-6048DiVA, id: diva2:978925
Note

Validerad; 2016; Nivå 2; 2016-12-02 (rokbeg)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2019-03-05Bibliographically approved

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Strömberg, Thomas

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