March  2013, 8(1): 23-35. doi: 10.3934/nhm.2013.8.23

Reaction-diffusion waves with nonlinear boundary conditions

1. 

Department of Mathematics, "Gheorghe Asachi" Technical University, Bd. Carol. I, 700506 Iasi, Romania

2. 

Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France

Received  January 2012 Revised  July 2012 Published  April 2013

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. Networks and Heterogeneous Media, 2013, 8 (1) : 23-35. doi: 10.3934/nhm.2013.8.23
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.

show all references

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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