Abstract
We consider the nonlinear diffusion equation
where
Here κ ≥ 0, λ > 0, ω ≥ 0, and 0 < ℓ ≤ ∞ are given constants, f: [0, ∞) → (0, ∞) is a decreasing Lipschitz function such that limr→∞ f(r) = 0, and p: [0, ℓ] × [0, ∞) → [0, ∞) is the unknown. Imposed are the boundary condition
,
for all t > 0 and the initial condition
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References
H. Ishii and I. Takagi, Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics. J. Math. Biol. 16, 1–24 (1982)
N. Shigesada and A. Okubo, Analysis of the self-shading effect on algal vertical distribution in natural waters. J. Math. Biol. 12, 311–326 (1981)
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© 1985 Springer-Verlag Berlin Heidelberg
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Ishii, H., Takagi, I. (1985). A Nonlinear Diffusion Equation in Phytoplankton Dynamics with Self-Shading Effect. In: Capasso, V., Grosso, E., Paveri-Fontana, S.L. (eds) Mathematics in Biology and Medicine. Lecture Notes in Biomathematics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93287-8_9
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DOI: https://doi.org/10.1007/978-3-642-93287-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15200-2
Online ISBN: 978-3-642-93287-8
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