Establishes verification theorem for optimal control of 2D/3D convective Brinkman-Forchheimer equations using strong solution theory and negative-order Sobolev estimates.
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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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A Verification Theorem for an Optimal Control Problem Governed by the Convective Brinkman--Forchheimer Equations
Establishes verification theorem for optimal control of 2D/3D convective Brinkman-Forchheimer equations using strong solution theory and negative-order Sobolev estimates.
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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.