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4 papers · 2 filters
Degenerate Elliptic PDEs on a Network with Kirchhoff Conditions
Guy Barles, Olivier Ley, Erwin Topp
In this article, we are interested in semilinear, possibly degenerate elliptic equations posed on a general network, with nonlinear Kirchhoff-type conditions for its interior verti…
Revisiting the blow-up criterion and the maximal existence time for solutions of the parabolic-elliptic Keller-Segel system in 2d-Euclidean space
Patrick Maheux, Vittoria Pierfelice
In this paper, we revisit the blow-up criteria for the simplest parabolic-elliptic (PKS) system in the 2D Euclidean space, including a consumption term. In the supercritical mass c…
Generalized principal eigenvalues for parabolic operators in bounded domains
Henri Berestycki, Grégoire Nadin, Luca Rossi
We introduce here new generalized principal eigenvalues for linear parabolic operators with heterogeneous coefficients in space and time. We consider a bounded spatial domain and a…
Optimisation of space-time periodic eigenvalues
Beniamin Bogosel, Idriss Mazari-Fouquer, Grégoire Nadin
The goal of this paper is to provide a qualitative analysis of the optimisation of space-time periodic principal eigenvalues. Namely, considering a fixed time horizon and the $…