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arXiv · 1403.1133

On the asymptotic shape of solutions to Neumann problems for non-cooperative parabolic systems

Alberto Saldaña·Tobias Weth
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Abstract

We consider a class of nonautonomous parabolic competition-diffusion systems on bounded radial domains under Neumann boundary conditions. We show that, if the initial profiles satisfy a reflection inequality with respect to a hyperplane, then global positive solutions are asymptotically (in time) foliated Schwarz symmetric with respect to antipodal points. Additionally, a related result for (positive and sign changing solutions) of a scalar equation with Neumann boundary conditions is given. The asymptotic shape of solutions to cooperative systems is also discussed.

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Alberto Saldaña, Tobias Weth. 2014-03-05. On the asymptotic shape of solutions to Neumann problems for non-cooperative parabolic systems. https://doi.org/10.1007/s10884-014-9395-9

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