Time regularity and long-time behavior of parabolic p-Laplace equations on infinite graphs

By Bobo Hua, Delio Mugnolo. 2014

53 citations recorded by the source corpus.

Abstract We consider the so-called discrete p-Laplacian, a nonlinear difference operator that acts on functions defined on the nodes of a possibly infinite graph. We study the corresponding Cauchy problem and identify the generator of the associated nonlinear semigroups. We prove higher order time regularity of the solutions. We investigate the long-time behavior of the solutions and discuss in particular finite extinction time and conservation of mass. Namely, on one hand, for small p if an infinite graph satisfies some isoperimetric inequality, then the solution to the parabolic p-Laplace equation vanishes in finite time; on the other hand, for large p, these parabolic p-Laplace equations always enjoy conservation of mass.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/058058ee0e91bd549a8800b12bb0673f7c9c32e8

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In Applied Mathematics

1. Matthias Keller
2. Michael Schwarz

In Mathematical Physics

1. Michael Schwarz
2. Matthias Keller
3. Daniel Lenz
4. Radoslaw K. Wojciechowski

Citations in the corpus

• The Kazdan–Warner equation on canonically compactifiable graphs (2017, methodology): “On the one hand this concerns non-linear operators such as the p-Laplacian [22,26,31], and on the other hand non-linear equations such as the Kazdan–Warner equation [13,16].”