Positive viscosity solutions of a third degree homogeneous parabolic infinity Laplace equation

Gang Li; Fen Gu; Feida Jiang

doi:10.3934/cpaa.2020071

Article Contents

2020, Volume 19, Issue 3: 1449-1462. Doi: 10.3934/cpaa.2020071

This issue Previous Article Asymptotic behavior of spherically or cylindrically symmetric solutions to the compressible Navier-Stokes equations with large initial data Next Article Fredholm theory for an elliptic differential operator defined on

$ \mathbb{R}^n $

and acting on generalized Sobolev spaces

Positive viscosity solutions of a third degree homogeneous parabolic infinity Laplace equation

College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

^* Corresponding author
^* Corresponding author

Received: March 31, 2019

Revised: July 31, 2019

Published: February 2020

This work was supported by National Natural Science Foundation of China (No. 11771214)

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Abstract

In this paper, we investigate positive viscosity solutions of a third degree homogeneous parabolic equation $ u^{2}u_{t} = \Delta_{\infty}u $. We prove a comparison principle, existence and uniqueness of continuous positive viscosity solutions.

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Mathematics Subject Classification: Primary: 35K55, 35K65; Secondary: 35D40.

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References

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