Ji, Shanming; Mei, Ming; Wang, Zejia Dirichlet problem for the Nicholson’s blowflies equation with density-dependent diffusion. (English) Zbl 1448.35311 Appl. Math. Lett. 103, Article ID 106191, 7 p. (2020). Summary: This paper is concerned with the time delayed Nicholson’s blowflies equation with degenerate diffusion. We prove the existence and uniqueness of the positive steady state solution under the Dirichlet boundary condition and we show the stability of the nontrivial steady state. Cited in 3 Documents MSC: 35K59 Quasilinear parabolic equations 35K65 Degenerate parabolic equations 35B35 Stability in context of PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 35Q92 PDEs in connection with biology, chemistry and other natural sciences 92D25 Population dynamics (general) Keywords:time delay; degenerate diffusion; Dirichlet problem; stability PDFBibTeX XMLCite \textit{S. Ji} et al., Appl. Math. Lett. 103, Article ID 106191, 7 p. (2020; Zbl 1448.35311) Full Text: DOI References: [1] Murry, J. D., Mathematical Biology I: An Introduction (2002), Springer: Springer New York, USA · Zbl 1006.92001 [2] Shiguesada, N.; Kawasaki, K.; Teramoto, E., Spatial segregation of interacting species, J. Theoret. Biol., 79, 83-99 (1979) [3] Aronson, D. G., Density-dependent interaction-diffusion systems, (Stewart, W. E.; Ray, W. H.; Conley, C. C., Dynamics and Modelling of Reactive Systems (1980), Academic Press: Academic Press New York), 161-176 [4] Matthysen, E., Density-dependent dispersal in birds and mammals, Ecography, 28, 403-416 (2005) [5] Hess, P., On uniqueness of positive solutions of nonlinear elliptic boundary value problems, Math. Z., 154, 17-18 (1977) · Zbl 0352.35046 [6] So, J. W.-H.; Yang, Y. J., Dirichlet Problem for the Diffusive Nicholson’s Blowflies Equation, J. Differential Equations, 150, 317-348 (1998) · Zbl 0923.35195 [7] Vàzquez, J. L., The Porous Medium Equation: Mathematical Theory (2006), Oxford Univ. Press [8] Wu, Z.; Zhao, J.; Yin, J.; Li, H., Nonlinear Diffusion Equations (2001), World Scientific Publishing Co. Put. Ltd. · Zbl 0997.35001 [9] Xu, T. Y.; Ji, S. M.; Mei, M.; Yin, J. X., Traveling waves for time-delayed reaction diffusion equations with degenerate diffusion, J. Differential Equations, 265, 4442-4485 (2018) · Zbl 1406.35087 [10] Xu, T. Y.; Ji, S. M.; Jin, C. H.; Mei, M.; Yin, J. X., Early and late stage profiles for a chemotaxis model with density-dependent jump probability, Math. Biosci. Eng., 15, 1345-1385 (2018) · Zbl 1416.92030 [11] Xu, T. Y.; Ji, S. M.; Mei, M.; Yin, J. X., On a chemotaxis model with degenerate diffusion: initial shrinking, eventual smoothness and expanding, J. Differential Equations, 268, 414-446 (2020) · Zbl 1442.35484 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.