On the vanishing contact structure for viscosity solutions of contact type Hamilton-Jacobi equations I: Cauchy problem

Kai Zhao; Wei Cheng

doi:10.3934/dcds.2019176

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2019, Volume 39, Issue 8: 4345-4358. Doi: 10.3934/dcds.2019176

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On the vanishing contact structure for viscosity solutions of contact type Hamilton-Jacobi equations I: Cauchy problem

Kai Zhao and
Wei Cheng^,

Department of Mathematics, Nanjing University, Nanjing 210093, China

^* Corresponding author: Wei Cheng
^* Corresponding author: Wei Cheng

Received: March 31, 2018

Revised: December 31, 2018

Published: May 2019

The authors are partly supported by Natural Scientific Foundation of China (Grant No. 11871267, No. 11631006 and No. 11790272)

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Abstract

We study the representation formulae for the fundamental solutions and viscosity solutions of the Hamilton-Jacobi equations of contact type. We also obtain a vanishing contact structure result for relevant Cauchy problems which can be regarded as an extension to the vanishing discount problem.

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Mathematics Subject Classification: Primary: 35F21, 49L25; Secondary: 37J50.

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References

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