We propose a level set method for systems of PDEs which is consistent with the previous research pursued by Evans (1996) for the heat equation and by Giga and Sato (2001) for Hamilton-Jacobi equations. Our approach follows a geometric construction related to the notion of barriers introduced by De Giorgi. The main idea is to force a comparison principle between manifolds of different codimension and require each nonzero sub-level of a solution of the level set equation to be a barrier for the graph of a solution of the corresponding system. We apply the method to a class of systems of first order quasi-linear equations. We compute the level set equation associated with suitable first order systems of conservation laws, with the mean curvature flow of a manifold of arbitrary codimension and with systems of reaction-diffusion equations.
Bellettini, G., Chermisi, M., & Novaga, M. (2007). The level set method for systems of PDEs. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 32(7), 1043-1064.
|Titolo:||The level set method for systems of PDEs|
|Citazione:||Bellettini, G., Chermisi, M., & Novaga, M. (2007). The level set method for systems of PDEs. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 32(7), 1043-1064.|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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