Singularly perturbed reaction-diffusion systems in cases of exchange of stabilities (Q2745397)
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scientific article; zbMATH DE number 1654638
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Singularly perturbed reaction-diffusion systems in cases of exchange of stabilities |
scientific article; zbMATH DE number 1654638 |
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24 February 2002
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two intersecting families of equilibria
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lower and upper solutions
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Singularly perturbed reaction-diffusion systems in cases of exchange of stabilities (English)
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In this paper the authors investigate singularly perturbed parabolic equations of the form: \(\varepsilon^2 (\partial_t u - \Delta u) = f(u,x,t,\varepsilon)\) as well as singularly perturbed elliptic equations of the form: \(\varepsilon^2 \Delta u = f(u,x,\varepsilon)\). The reduced equation \(f(u,x,0)=0\) is assumed to have two intersecting families of equilibria. Using the method of lower and upper solutions the authors show the existence of a solution and its asymptotic behavior as \(\varepsilon\to 0\).
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