On dual solutions occurring in mixed convection in a porous medium. (English) Zbl 0597.76081

Summary: The dual solutions to an equation, which arose previously in mixed convection in a porous medium, occurring for the parameter \(\alpha\) in the range \(0<\alpha <\alpha_ 0\) are considered. It is shown that the lower branch of solutions terminates at \(\alpha =0\) with an essential singularity. It is also shown that both branches of solutions bifurcate out of the single solution at \(\alpha =\alpha_ 0\) with an amplitude proportional to \((\alpha_ 0-\alpha)^{1/2}\). Then, by considering a simple time-dependent problem, it is shown that the upper branch of solutions is stable and the lower branch unstable, with the change in temporal stability at \(\alpha =\alpha_ 0\) being equivalent to the bifurcation at that point.


76Rxx Diffusion and convection
76S05 Flows in porous media; filtration; seepage
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