$L^∞$-energy method for a parabolic system with convection and hysteresis effect

Emil Minchev; Mitsuharu Ôtani

doi:10.3934/cpaa.2018077

Article Contents

2018, Volume 17, Issue 4: 1613-1632. Doi: 10.3934/cpaa.2018077

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$L^∞$-energy method for a parabolic system with convection and hysteresis effect

Emil Minchev^1, and
Mitsuharu Ôtani^2, ,

1.
Hikari Ltd, P.O. Box 85 Ruse 7000, Bulgaria
2.
Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

* Corresponding author
* Corresponding author

Received: March 2017

Revised: October 2017

Published: April 2018

The second author is supported by the Grant-in-Aid for Scientific Research #15K13451, the Ministry of Education, Culture, Sports, Science, and Technology, Japan.

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Abstract

The $L^∞$-energy method is developed so as to handle nonlinear parabolic systems with convection and hysteresis effect. The system under consideration originates from a biological model where the hysteresis and convective effects are taken into account in the evolution of species. Some results for the existence of local and global solutions as well as the uniqueness of solution are presented.

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Mathematics Subject Classification: Primary: 35R70, 35K51; Secondary: 37N25, 47J40.

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References

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