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Excess action and broken characteristics for Hamilton-Jacobi equations
Luleå University of Technology.
Mälardalen University, School of Innovation, Design and Engineering, Innovation and Product Realisation.ORCID iD: 0000-0002-8524-3321
2014 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 110, 113-129 p.Article in journal (Refereed) Published
Abstract [en]

We study propagation of singularities for Hamilton-Jacobi equations S t+H(t,x,λS)=0,(t,x)∈(0,∞)×ℝn, by means of the excess Lagrangian action and a related class of characteristics. In a sense, the excess action gauges how far a curve X(t) is from being action minimizing for a given viscosity solution S(t,x) of the Hamilton-Jacobi equation. Broken characteristics are defined as curves along which the excess action grows at the slowest pace possible. In particular, we demonstrate that broken characteristics carry the singularities of the viscosity solution.

Place, publisher, year, edition, pages
2014. Vol. 110, 113-129 p.
Keyword [en]
Generalized characteristic, Hamilton-Jacobi equation, Propagation of singularities, Mathematical techniques, Nonlinear analysis, Hamilton Jacobi equations, Lagrangian, Viscosity solutions, Mechanics
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:mdh:diva-25906DOI: 10.1016/j.na.2014.08.001ISI: 000342386300009Scopus ID: 2-s2.0-84906675945OAI: oai:DiVA.org:mdh-25906DiVA: diva2:746338
Available from: 2014-09-12 Created: 2014-09-12 Last updated: 2015-02-02Bibliographically approved

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Ahmadzadeh, Farzaneh
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