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arXiv · 2404.04342

On the well-posedness of some model arising in the mathematical biology

Messoud Efendiev·Vitali Vougalter
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Abstract

In the article we establish the global well-posedness in W^{1, 2, 2}(R\times R^{+}) of the integro-differential equation in the case of the anomalous diffusion when the one dimensional negative Laplace operator is raised to a fractional power in the presence of the transport term. The model is relevant to the cell population dynamics in the Mathematical Biology. Our proof relies on a fixed point technique.

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Messoud Efendiev, Vitali Vougalter. 2024-04-05. On the well-posedness of some model arising in the mathematical biology. https://arxiv.org/abs/2404.04342

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