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NTIS 바로가기Kyungpook mathematical journal, v.63 no.2, 2023년, pp.141 - 154
Min-Gi Lee (Department of Mathematics, Kyungpook National University)
We study the stability of traveling waves of a certain chemotaxis model. The traveling wave solution is a central object of study in a chemotaxis model. Kim et al. [8] introduced a model on a population and nutrient densities based on a nonlinear diffusion law. They proved the existence of traveling...
M. Alfaro, T. Giletti, Y. -J. Kim, G. Peltier and H. Seo, On the modelling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of?individuals, J. Math. Biol., 84(2022), 1-35.
L. Desvillettes, P. Laurencot, A. Trescases and M. Winkler, Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing, Nonlinear?Analysis, 226(2023), 113153.
K. Fujie and J. Jiang, Boundedness of classical solutions to a degenerate Keller-Segel?type model with signal-dependent motilities, Acta Appl. Math., 176(3)(2021), 1-36.
E. F. Keller and L. A. Segel, Traveling bands of chemotactic bacteria: a theoretical?analysis, J. Theor. Biol., 30(2)(1971), 235-248.
H. -Y. Kim, Y. -J. Kim and H. -J. Lim, Heterogeneous discrete kinetic model and its?diffusion limit, Kinet. Relat. Models, 14(5)(2021), 749-765.
J. Chung, Y-J Kim and M-G Lee, Random walk with heterogeneous sojourn time,?arXiv preprint 2302.06275 (2023).
Y-J Kim and C. Yoon, Modeling bacterial traveling wave patterns with exact cross-diffusion and population growth, Discrete Contin. Dyn. Syst. - B (2023).
Y-J Kim, M. Mimura and C. Yoon, Nonlinear diffusion for bacterial traveling wave?phenomenon, Bull. Math. Biol., 85(5)(2023), 27 pp.
W. Lyu and Z.-A. Wang, Global classical solutions for a class of reaction-diffusion?system with density-suppressed motility, Electron. res. arch., 30(3)(2022), 995-1015.
Y. Tao and M. Winkler, Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension, J.?Differential Equations, 343(2023), 390-418.
Z. -A. Wang and J. Zheng, Global boundedness of the fully parabolic Keller-Segel?system with signal-dependent motilities, Acta Appl. Math., 171(2021), 1-19.
M. Winkler, Global generalized solvability in a strongly degenerate taxis-type?parabolic system modeling migration-consumption interaction, Z. Angew. Math.?Phys., 74(1)(2023), 20pp.
M. Winkler, Can simultaneous density-determined enhancement of diffusion and?cross-diffusion foster boundedness in Keller-Segel type systems involving signal-dependent motilities?, Nonlinearity, 33(12)(2020), 6590--6623.
C. Yoon and Y-J Kim, Bacterial chemotaxis without gradient-sensing, J. Math. Biol.,?70(2015), 1359-1380.
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