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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.

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