Quasilinear reaction diffusion systems with mass dissipation

Evangelos Latos; Takashi Suzuki; Evangelos Latos; Takashi Suzuki

doi:10.3934/mine.2022042

Mathematics in Engineering

2022, Volume 4, Issue 5: 1-13. doi: 10.3934/mine.2022042

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Quasilinear reaction diffusion systems with mass dissipation

Evangelos Latos ¹,
Takashi Suzuki ^{2
,
,}

1.
Institut für Mathematik und Wissenschaftliches Rechnen, Heinrichstraße 36, 8010 Graz, Austria
2.
Center for Mathematical Modeling and Data Science, Osaka University, Japan

Received: 29 December 2020 Accepted: 12 July 2021 Published: 19 October 2021

We study quasilinear reaction diffusion systems relative to the Shigesada-Kawasaki-Teramoto model. Nonlinearity standing for the external force is provided with mass dissipation. Estimate in several norms of the solution is provided under the restriction of diffusion coefficients, growth rate of reaction, and space dimension.
- quasilinear reaction diffusion system,
- total mass dissipation,
- global in time classical solution,
- Shigesada-Kawasaki-Teramoto model
Citation: Evangelos Latos, Takashi Suzuki. Quasilinear reaction diffusion systems with mass dissipation[J]. Mathematics in Engineering, 2022, 4(5): 1-13. doi: 10.3934/mine.2022042

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Abstract

We study quasilinear reaction diffusion systems relative to the Shigesada-Kawasaki-Teramoto model. Nonlinearity standing for the external force is provided with mass dissipation. Estimate in several norms of the solution is provided under the restriction of diffusion coefficients, growth rate of reaction, and space dimension.

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