4 problems

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Optimal decay estimate for active Brownian particle models
Optimal-decay conjecture. The estimate obtained in the paper is optimal; equivalently, the stability conditions should not in general be extendable to the scales…
Conjectureopenactive-brownian-particles stability-analysis volterra-equationsarXiv posted 2 days ago
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Dominance of the perturbation in the supercritical forcing regime
Consider the forced Volterra equation with forcing term $H(t)$ and define $F_U$ as the function used in the source's growth-rate criterion. Suppose the nonlinearity satisfies the s…
Conjectureopenasymptotic-analysis integral-equations volterra-equationsarXiv posted 2 days ago
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Asymptotic negligibility of the delayed term in superlinear Volterra equations
Let $f$ be the nonlinearity in the Volterra equation and in the bounded-delay comparison equation, and suppose that … The delayed term in the associated second-order equation shoul…
Conjectureopenblow-up delay-differential-equations volterra-equationsarXiv posted 2 days ago
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Conjecture that stationarity of the forcing implies asymptotic stationarity of the solution
Stationarity-to-asymptotic-stationarity conjecture. Stationarity in $H$ implies asymptotic stationarity in $x$ .
Conjectureopenstationarity stochastic-processes volterra-equationsarXiv posted 2 days ago

Optimal decay estimate for active Brownian particle models