Talk:Viscosity solution

Front evolution?
What does 'front evolution' mean? Is it a concept from fluid dynamics? Could someone knowledgeable provide an appropriate link please? --Rinconsoleao (talk) 14:03, 9 June 2008 (UTC)


 * Front evolution or front propagation is quite general, it applies to optics, to the simulation of combustion and even to image recognition. Souganidis has a book about it http://www.springerlink.com/content/945754087q296357 . It occurs in many nonlinear PDE problems where  there are two areas of space separated by a surface (the front) and that front can move.  Encyclops (talk) 22:57, 10 June 2008 (UTC)

Uniqueness of solution
I was just wondering about the uniqueness of the viscosity solution. Most PDEs can be proven to have a unique solution. What about the viscosity solution? Are they unique, or are there multiple viscosity solutions to a given PDE? (this will probably depend on the PDE in question, but some info on it would be appreciated). 131.155.59.211 (talk) 10:03, 7 January 2010 (UTC)


 * I don't know if you care six or so months later, but yes, there is a unique viscosity solution for PDEs of the form $$u+H(x,\nabla u) = 0$$, given that H is uniformly continuous in x. I'm not sure whether a more general uniqueness theorem holds though, for general PDEs —Preceding unsigned comment added by 202.124.73.249 (talk) 10:46, 15 August 2010 (UTC)

Semijets
In the literature (I'm just reading to understand the concept, I admit) there is also often talk about a reformulation of the definition in terms of semijets. See for instance Michael G. Crandall, Hitoshi Ishii, and Pierre-Louis Lions: User's Guide to Viscosity Solutions of Second Order Partial Differential Equations. This concept seems to have advantages for some calculations involving viscosity solutions. Would it be interesting to add a section about the definition of the semijets plus redirect to it (there's nothing found at the moment when looking for that term!) and the reformulation? I'd be willing to write it after I understand the matter sufficiently (including of course literature citations as appropriate), if this is deemed a useful addition. Domob (talk) 10:40, 18 October 2012 (UTC)