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

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    * Corresponding author
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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  • 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.

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


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