On the exterior problem for parabolic k-Hessian equations

Ziwei Zhou; Jiguang Bao

doi:10.3934/cpaa.2022106

Article Contents

2022, Volume 21, Issue 10: 3407-3420. Doi: 10.3934/cpaa.2022106

This issue Previous Article On the exponential time-decay for the one-dimensional wave equation with variable coefficients Next Article On the optimal decay rate of the weakly damped wave equation

On the exterior problem for parabolic k-Hessian equations

Ziwei Zhou^1, and
Jiguang Bao^2, ,

1.
School of Statistics, University of International Business and Economics, Beijing 100029, China
2.
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

^* Corresponding author
^* Corresponding author

Received: December 31, 2021

Revised: April 30, 2022

Early access: June 2022

Published: October 2022

The first author is supported by "the Fundamental Research Funds for the Central Universities" in UIBE (21QD20). The second author is supported in part by the NSFC (11871102)

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Abstract

We use Perron method to prove the existence of ancient solutions of the exterior problem for parabolic k-Hessian equations $ -u_tS_k(D^2u) = 1 $ with prescribed asymptotic behavior at infinity.

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Mathematics Subject Classification: Primary: 35K55, 35A01.

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References

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