# American Institute of Mathematical Sciences

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 & Heterogeneous Media, 2013, 8 (1) : 23-35. doi: 10.3934/nhm.2013.8.23
##### References:
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##### 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.  Google Scholar [2] A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice-Hall, Englwood Cliffs, 1964.  Google Scholar [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.  Google Scholar [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.  Google Scholar [5] A. Volpert, Vit. Volpert and Vl. Volpert, "Traveling Wave Solutions of Parabolic Systems," Translation of Mathematical Monographs, 140, Amer. Math. Society, Providence, 1994.  Google Scholar [6] V. Volpert and A. Volpert, Spectrum of elliptic operators and stability of travelling waves, Asymptotic Analysis, 23 (2000), 111-134.  Google Scholar [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.  Google Scholar
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