Large-time asymptotics of a public goods game model with diffusion

Klemens Fellner; Evangelos Latos; Takashi Suzuki

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arXiv · 1808.02117

Large-time asymptotics of a public goods game model with diffusion

Klemens Fellner·Evangelos Latos·Takashi Suzuki

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Abstract

We consider a spatially inhomogeneous public goods game model with diffusion. By utilising a generalised Hamiltonian structure of the model we study the existence of global classical solutions as well as the large time behaviour: First, the asymptotic convergence of the PDE to the corresponding ODE system is proven. This result entails also the periodic behaviour of PDE solutions in the large time limit. Secondly, a shadow system approximation is considered and the convergence of the PDE to the shadow system in the associated fast-diffusion limit is shown. Finally, the asymptotic convergence of the shadow to the ODE system is proven.

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Klemens Fellner, Evangelos Latos, Takashi Suzuki. 2018-08-06. Large-time asymptotics of a public goods game model with diffusion. https://arxiv.org/abs/1808.02117

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