A1 Journal article (refereed)
Asymptotic behavior of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian (2009)

Akagi, G., Juutinen, P., & Kajikiya, R. (2009). Asymptotic behavior of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian. Mathematische Annalen, 343(4), 921-953. https://doi.org/10.1007/s00208-008-0297-1

JYU authors or editors

Publication details

All authors or editors: Akagi, Goro; Juutinen, Petri; Kajikiya, Ryuji

Journal or series: Mathematische Annalen

ISSN: 0025-5831

eISSN: 1432-1807

Publication year: 2009

Volume: 343

Issue number: 4

Pages range: 921-953

Publisher: Springer Nature

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s00208-008-0297-1

Publication open access: Not open

Publication channel open access: 

Abstract

The asymptotic behavior of viscosity solutions to the Cauchy–Dirichlet problem for the degenerate parabolic equation ut = ∆∞u in Ω × (0,∞), where ∆∞ stands for the so-called infinity-Laplacian, is studied in three cases: (i) Ω = RN and the initial data has a compact support; (ii) Ω is bounded and the boundary condition is zero; (iii) Ω is bounded and the boundary condition is non-zero. Our method of proof is based on the comparison principle and barrier function arguments. Explicit representations of separable type and self-similar type of solutions are also established. Moreover, in case (iii), we propose another type of barrier function deeply related to a solution of ∆∞φ = 0.

Keywords: differential calculus

Free keywords: asymptotic behavior; infinity Laplacian

Contributing organizations

Ministry reporting: Yes

Preliminary JUFO rating: Not rated