Reaction-diffusion waves with nonlinear boundary conditions
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Department of Mathematics, "Gheorghe Asachi" Technical University, Bd. Carol. I, 700506 Iasi
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2.
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne
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Received:
01 January 2012
Revised:
01 July 2012
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Primary: 35K57; Secondary: 35J60.
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A reaction-diffusion equation with nonlinear boundary condition is
considered in a two-dimensional infinite strip. Existence of
waves in the bistable case is proved by the Leray-Schauder
method.
Citation: Narcisa Apreutesei, Vitaly Volpert. Reaction-diffusion waves with nonlinear boundary conditions[J]. Networks and Heterogeneous Media, 2013, 8(1): 23-35. doi: 10.3934/nhm.2013.8.23
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Abstract
A reaction-diffusion equation with nonlinear boundary condition is
considered in a two-dimensional infinite strip. Existence of
waves in the bistable case is proved by the Leray-Schauder
method.
References
|
[1]
|
A. Fabiato, Calcium-induced release of calcium from the cardiac sarcoplasmic reticulum, Am. J. Physiol. Cell. Physiol., 245 (1983), 1-14. doi: 10.1016/0022-2828(92)90114-F
|
|
[2]
|
A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice-Hall, Englwood Cliffs, 1964.
|
|
[3]
|
N. El Khatib, S. Genieys, B. Kazmierczak and V. Volpert, Reaction-diffusion model of atherosclerosis development, J. Math. Biol., 65 (2012), 349-374. doi: 10.1007/s00285-011-0461-1
|
|
[4]
|
M. Kyed, Existence of travelling wave solutions for the heat equation in infinite cylinders with a nonlinear boundary condition, Math. Nachr., 281 (2008), 253-271. doi: 10.1002/mana.200710599
|
|
[5]
|
A. Volpert, Vit. Volpert and Vl. Volpert, "Traveling Wave Solutions of Parabolic Systems," Translation of Mathematical Monographs, 140, Amer. Math. Society, Providence, 1994.
|
|
[6]
|
V. Volpert and A. Volpert, Spectrum of elliptic operators and stability of travelling waves, Asymptotic Analysis, 23 (2000), 111-134.
|
|
[7]
|
V. Volpert, "Elliptic Partial Differential Equations. Volume 1. Fredholm Theory of Elliptic Problems in Unbounded Domains," Birkhäuser, Basel, 2011. doi: 10.1007/978-3-0346-0537-3
|
-
-
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