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Well-posedness for the system of the Hamilton-Jacobi and the continuity equations
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2007 (English)In: Journal of evolution equations (Printed ed.), ISSN 1424-3199, E-ISSN 1424-3202, Vol. 7, no 4, p. 669-700Article in journal (Refereed) Published
Abstract [en]

Let H (t, x, p) be a Hamiltonian function that is convex in p. Let the associated Lagrangian satisfy the nonstandard minorization condition where m > 0, ω > 0, and C ≥ 0 are constants. Under some additional conditions, we prove that the associated value function is the unique viscosity solution of S t + H(t, x, ∇S) = 0 in , without any conditions at infinity on the solution. Here ωT < π/2. To the Hamilton-Jacobi equation corresponding to the classical action integrand in mechanics, we adjoin the continuity equation and establish the existence and uniqueness of a viscosity-measure solution (S, ρ) of ...This system arises in the WKB method. The measure solution is defined by means of the Filippov flow of ∇S.

Place, publisher, year, edition, pages
2007. Vol. 7, no 4, p. 669-700
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-11087DOI: 10.1007/s00028-007-0327-6ISI: 000251578600004Scopus ID: 2-s2.0-38749122862Local ID: 9fedd940-6b46-11dc-9e58-000ea68e967bOAI: oai:DiVA.org:ltu-11087DiVA, id: diva2:984036
Note
Validerad; 2007; 20070925 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Strömberg, Thomas

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