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WELL-POSEDNESS RESULTS FOR GENERAL REACTION–DIFFUSION TRANSPORT OF OXYGEN IN ENCAPSULATED CELLS

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  18 October 2024

YUMA NAKAMURA Open the ORCID record for YUMA NAKAMURA [Opens in a new window] ,
KHARISMA SURYA PUTRI Open the ORCID record for KHARISMA SURYA PUTRI [Opens in a new window] ,
ALEF EDOU STERK Open the ORCID record for ALEF EDOU STERK [Opens in a new window]  and
THOMAS GEERT DE JONG Open the ORCID record for THOMAS GEERT DE JONG [Opens in a new window]
YUMA NAKAMURA
Affiliation:
Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa, Japan e-mail: [email protected]
KHARISMA SURYA PUTRI
Affiliation:
Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa, Japan e-mail: [email protected]
ALEF EDOU STERK
Affiliation:
Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, The Netherlands e-mail: [email protected]
THOMAS GEERT DE JONG*
Affiliation:
Faculty of Mathematics and Physics, Kanazawa University, Kanazawa, Ishikawa, Japan
*
e-mail: [email protected]
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Abstract

We provide well-posedness results for nonlinear parabolic partial differential equations (PDEs) given by reaction–diffusion equations describing the concentration of oxygen in encapsulated cells. The cells are described in terms of a core and a shell, which introduces a discontinuous diffusion coefficient as the material properties of the core and shell differ. In addition, the cells are subject to general nonlinear consumption of oxygen. As no monotonicity condition is imposed on the consumption, monotone operator theory cannot be used. Moreover, the discontinuity in the diffusion coefficient bars us from applying classical results on strong solutions. However, by directly applying a Galerkin method, we obtain uniqueness and existence of the strong form solution. These results provide the basis to study the dynamics of cells in critical states.

Keywords

parabolic PDEreaction–diffusiondiffraction problemcore–shell geometryGalerkin approximation

MSC classification

Primary: 35K57: Reaction-diffusion equations
Secondary: 35K55: Nonlinear parabolic equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 111 , Issue 1 , February 2025 , pp. 154 - 163
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This work is supported by JST CREST Grant Number JPMJCR2014.

References

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