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arXiv · 1508.06149

On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics

Nikos I. Kavallaris·Johannes Lankeit·Michael Winkler
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Abstract

We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for \[ u_t = u Δu + u \int_Ω|\nabla u|^2 \] in bounded domains $Ω\subset\mathbb{R}^n$ and prove that solutions converge to $0$ if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. We show that in this case the blow-up set coincides with $\overlineΩ$, i.e. the finite-time blow-up is global. Key words: Degenerate diffusion, non-local nonlinearity, blow-up, evolutionary games, infinite dimensional replicator dynamics

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Nikos I. Kavallaris, Johannes Lankeit, Michael Winkler. 2015-08-25. On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics. https://arxiv.org/abs/1508.06149

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