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

被引：0
|
作者：
Efendiev, Messoud [1 ,2 ]
Vougalter, Vitali [3 ]
机构：
[1] Helmholtz Zent Munchen, Inst Computat Biol, Neuherberg, Germany
[2] Marmara Univ, Dept Math, Istanbul, Turkiye
[3] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年
基金：
加拿大自然科学与工程研究理事会;
关键词：
integro-differential equations; Sobolev spaces; well-posedness; ANOMALOUS DIFFUSION; TRAVELING-WAVES;
D O I：
10.1002/mma.10507
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the article, we establish the global well-posedness in W-1,W-2,W-2(R x R+) of the integro-differential equation in the case of 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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页数：12
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