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Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations

Authors
  • Dai, Limei1
  • Bao, Jiguang2
  • 1 Weifang University, Shandong 261061 , (China)
  • 2 Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875 , (China)
Type
Published Article
Journal
Advanced Nonlinear Studies
Publisher
De Gruyter
Publication Date
Aug 06, 2020
Volume
20
Issue
4
Pages
769–781
Identifiers
DOI: 10.1515/ans-2020-2102
Source
De Gruyter
Keywords
License
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Abstract

In this paper, we study the Cauchy problem of the parabolic Monge–Ampère equation -ut⁢det⁡D2⁢u=f⁢(x,t)-u_{t}\det D^{2}u=f(x,t) and obtain the existence and uniqueness of viscosity solutions with asymptotic behavior by using the Perron method.

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