The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system (Q932282)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system |
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The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system (English)
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10 July 2008
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The authors consider an Allen-Cahn type equation of the form \(u_{t}=\triangle u+\varepsilon^{-2}f^{\varepsilon}(x,t,u)\), where \(\varepsilon\) is a small parameter and \(f^{\varepsilon}(x,t,u)=f(u)-\varepsilon g^{\varepsilon}(x,t,u)\) a bistable nonlinearity associated with a double-well potential whose well-depths can be slightly unbalanced.
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nonlinear PDE
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reaction-diffusion system
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singular perturbation
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Allen-Cahn
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FitzHugh-Nagumo
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interface motion
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bistable nonlinearity
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double-well potential
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