19 problems

Consider the minimally bistable ERK subnetwork, and let a compatibility class be determined by the conserved quantities of the reaction system. Three-steady-state conjecture. For e…

Let $\mathcal{C}$ be the upper cell order, and consider the physical solutions of the evolution equations … A solution is physical when the state variables are real and nonnegative…

Let $\mathcal{C}$ be the upper cell order, and let the reaction rates be constant choices of the parameters entering the steady-state equations. A solution is physical when the cor…

Let $\mathcal{C}$ be the upper cell order, and consider the steady states of the granular-system evolution equations. A steady state satisfies detailed balance when the forward and…

Let $\mathcal{C}>5$ be the upper cell order, and let $\bar{\eta}_{i,j}$ denote the finite fluxes determined by the steady-state equations. A steady state satisfies detailed balance…

A chemical reaction network is a system of chemical species and reactions whose steady states are solutions of its associated mass-action equations; a steady state is positive when…

Infinitely-many-steady-states conjecture. Some models may have infinitely many piecewise-constant steady states.

Let $\Omega=B_R(0)\subset\mathbb{R}^2$ with $R>0$ and $k>0$. A steady state is a solution $(u,v)$ of the stationary problem considered in the paper, with prescribed mass…

Consider the full ERK network and the same network with $k_{\mathrm{on}}=0$, and let a positive steady state mean a steady state with all relevant concentrations positive; call a s…

Three-steady-state conjecture. The maximum possible number of positive steady states of this reaction network is three. This includes the parameter regimes in which either $a_+>1$…

Let $G$ be a reaction network consisting of one reversible-reaction pair $y\leftrightarrows y'$ and one irreversible reaction $\widetilde y\to\widetilde y'$. The reaction vectors a…

Let $G$ be a reaction network, and suppose that $G$ does not admit infinitely many positive steady states in any stoichiometric compatibility class. Recall that $G$ admits $k$ posi…

Let $\Lambda$ be the spatial domain, and consider the kinetic models in which thermal reservoirs act uniformly throughout $\Lambda$ rather than only at its boundary. A nonequilibri…

Nondegeneracy conjecture. Every network with finitely many positive steady states has the same capacity when capacity is counted using all positive steady states or only nondegener…

For positive integers $m\geq 2$ and $n\geq 2$, let $K_{m,n}$ be the sequestration network … and let $\widetilde{K}_{m,n}$ be its fully open extension, obtained by adjoining all inf…

Let $n\geq 1$ and consider the multiple futile cycle network with substrates $S_0,\ldots,S_n$ and enzymes $E$ and $F$, in which $E$ facilitates the forward transitions and $F$ the…

A weakly reversible network is a chemical reaction network whose reaction graph has the property that every reaction lies in a strongly connected component. A positive steady state…

Let $J_{\alpha}(t)$ denote the current in lead or channel $\alpha$ at time $t$. The ergodic-limit conjecture. Even in the general interacting case, performing the ergodic limit … s…

The evolution system has conserved total mass … The discussion concerns steady states and critical points of the entropy functional for dimensions where global minimizers may or ma…