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A system of the Hamilton-Jacobi and the continuity equations in the vanishing viscosity limit
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2011 (English)In: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 10, no 2, p. 479-506Article in journal (Refereed) Published
Abstract [en]

We study the following system of the viscous Hamilton-Jacobi and the continuity equations in the limit as epsilon down arrow 0: S-t(epsilon) + 1/2 vertical bar DS epsilon vertical bar(2) + V(x) - epsilon Delta S-epsilon = 0 in Q(T), S-epsilon(0, x) = S-0(x) in R-n; rho(epsilon)(t) + div(rho(epsilon) DS epsilon) = 0 in Q(T), rho(epsilon)(0, x) = rho(0)(x) in R-n. Here Q(T) = (0, T] x R-n. The potential V and the initial function S-0 are allowed to grow quadratically while rho(0) is a Borel measure. The paper justifies and describes the vanishing viscosity transition to the corresponding inviscid system. The notion of weak solution employed for the inviscid system is that of a viscosity-measure solution (S, rho).

Place, publisher, year, edition, pages
2011. Vol. 10, no 2, p. 479-506
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-7815DOI: 10.3934/cpaa.2011.10.479ISI: 000285790600005Scopus ID: 2-s2.0-82155186063Local ID: 63b77220-8695-11df-8806-000ea68e967bOAI: oai:DiVA.org:ltu-7815DiVA, id: diva2:980705
Note
Validerad; 2011; 20100703 (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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  • apa
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