Traveling wave solutions for bistable differential-difference equations with periodic diffusion (Q2706097)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Traveling wave solutions for bistable differential-difference equations with periodic diffusion |
scientific article |
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19 March 2001
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propagation failure
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bistable equation
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nonlinear spatially discrete diffusion equations
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Fourier transform
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bifurcation
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Traveling wave solutions for bistable differential-difference equations with periodic diffusion (English)
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Problems that are modeled by nonlinear spatially discrete diffusion equations occur in the material sciences (crystal growth, interface motion in crystalline materials, spinoidal decomposition, grain boundary movement in thin films), biology (the bidomain model for cardiac tissue, tissue filtration, gas exchange in lungs, calcium waves), etc. The authors provide an analytical solution using the Fourier transform for the case when the bistable nonlinearity is represented by the piecewise linear function. Numerical studies for the time evolution of the traveling waves are presented. Some results concerning type of bifurcation are obtained.
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