Quantitative Compactness Estimates for Hamilton–Jacobi Equations View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2016-02

AUTHORS

Fabio Ancona, Piermarco Cannarsa, Khai T. Nguyen

ABSTRACT

We study quantitative compactness estimates in Wloc1,1 for the map St, t>0 that is associated with the given initial data u0∈Lip(RN) for the corresponding solution Stu0 of a Hamilton–Jacobi equation ut+H(∇xu)=0,t≥0,x∈RN,with a uniformly convex Hamiltonian H=H(p). We provide upper and lower estimates of order 1/εN on the Kolmogorov ε-entropy in W1,1 of the image through the map St of sets of bounded, compactly supported initial data. Estimates of this type are inspired by a question posed by Lax (Course on Hyperbolic Systems of Conservation Laws. XXVII Scuola Estiva di Fisica Matematica, Ravello, 2002) within the context of conservation laws, and could provide a measure of the order of “resolution” of a numerical method implemented for this equation. More... »

PAGES

793-828

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00205-015-0907-5

DOI

http://dx.doi.org/10.1007/s00205-015-0907-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1010063101


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