Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system

Karoline Disser

doi:10.3934/dcdss.2020326

Article Contents

2021, Volume 14, Issue 1: 321-330. Doi: 10.3934/dcdss.2020326

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Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system

Karoline Disser

FB Mathematik, TU Darmstadt, Schlossgartenstr. 7, 64293 Darmstadt, Germany

Dedicated to Alexander Mielke on the occasion of his 60th birthday

Received: April 2019

Revised: November 2019

Early access: April 2020

Published: January 2021

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Abstract

We prove a global existence, uniqueness and regularity result for a two-species reaction-diffusion volume-surface system that includes nonlinear bulk diffusion and nonlinear (weak) cross diffusion on the active surface. A key feature is a proof of upper $ L^{\infty} $-bounds that exploits the entropic gradient structure of the system.

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Mathematics Subject Classification: Primary: 35K61, 35K57; Secondary: 35B45, 35A01.

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References

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