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On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics
Kavallaris, Nikos I. Lankeit, Johannes Winkler, Michael
Kavallaris, Nikos I.
Lankeit, Johannes
Winkler, Michael
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2017-03-28
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Abstract
We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for
\[
u_t = u \Delta u + u \int_\Omega |\nabla u|^2
\]
in bounded domains $\Om\sub\R^n$ which arises in game theory. We 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. In particular, it is shown that in this case the blow-up set coincides with $\overline{\Omega}$, i.e. the finite-time blow-up is global.
Citation
Kavallaris, N. I., Lankeit, J., & Winkler, M. (2017). On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics. SIAM Journal on Mathematical Analysis, 49(2), 954-983. DOI: 10.1137/15M1053840
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SIAM
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SIAM Journal on Mathematical Analysis
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en
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0036-1410