Authors prove a minimax theorem for bilinear transport from zero-sum games, derive an explicit endpoint cost below critical interaction strength, and show the resulting NMK plans admit Monge solutions given by gradients of convex or concave functions.
On general minimax theorems.Pacific Journal of Mathematics, 8(1):171–176, 1958.https: //projecteuclid.org/euclid.pjm/1103040253
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For the given chemotaxis model, uniform persistence holds when m ≥ 1; the positive equilibrium is linearly stable for χ0 below a parameter-dependent threshold χ*(u*) and unstable above it, with exponential convergence under stated conditions.
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Chemotaxis models with signal-dependent sensitivity and a logistic-type source, II: Persistence and stabilization
For the given chemotaxis model, uniform persistence holds when m ≥ 1; the positive equilibrium is linearly stable for χ0 below a parameter-dependent threshold χ*(u*) and unstable above it, with exponential convergence under stated conditions.