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VOL. 85 | 2020 On an obstacle problem arising in large exponent asymptotics for one dimensional fully nonlinear diffusions of power type
Qing Liu

Editor(s) Yoshikazu Giga, Nao Hamamuki, Hideo Kubo, Hirotoshi Kuroda, Tohru Ozawa

Abstract

In this note, we discuss the limit behavior for a fully nonlinear diffusion equation of power type in one space dimension. It turns out that, when the initial value is Lipschitz and convex, the solution converges locally uniformly to a unique limit function that is independent of the time variable as the exponent tends to infinity. We characterize the limit as the minimal solution of an obstacle problem. Such asymptotic behavior is closely related to applications in mathematical models of image denoising and collapsing sandpiles.

Information

Published: 1 January 2020
First available in Project Euclid: 29 December 2020

Digital Object Identifier: 10.2969/aspm/08510281

Subjects:
Primary: 35K55
Secondary: 35B40, 35D40

Rights: Copyright © 2020 Mathematical Society of Japan

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