Singularly perturbed reaction-diffusion systems in cases of exchange of stabilities (Q2745397)

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 \(\varepsilon\to 0\).