9 problems

Let $p\in(0,1]$, let $A_{p,n}$ be the total gelation time, and let $U_{p,n}$ denote the number of unicycle components at time $A_{p,n}$. Krapivsky's conjecture. … This conjecture c…

Let $K:(0,\infty)^2\to[0,\infty)$ be a coagulation kernel. It is $\gamma$-homogeneous when … for all $\lambda,x,y>0$, and gelation is the loss of mass from finite-mass particles th…

Consider the discrete coagulation-fragmentation equation with multiplicative coagulation and constant fragmentation kernels, and let $\rho_0$ be initial data satisfying the paper's…

Let $K:(0,\b7infty)\times(0,\infty)\to[0,\infty)$ be a coagulation kernel and let $\kappa>0$. A kernel is called non-gelling if all solutions conserve mass, and gelling if mass con…

Fix a homogeneity exponent $\gamma>1$. For parameters $a,b$ satisfying … consider the self-similar profile equation … Here a solution is physically relevant when it corresponds to…

Finite-time gelation conjecture. Gelation occurs in finite time. The preceding results establish local solutions for faster-growing kernels, while heuristic studies suggest that…

Let the exchange-driven growth system have a symmetric interaction kernel satisfying a growth bound with exponents $c0,bd ottextgreater0$ and $3<c0+bd ottextless4$, in the intermed…

Let $K$ be the coagulation kernel and $a$ the overall breakup rate, given by … … where $\alpha\leq\beta\leq 1$, $\lambda:=\alpha+\beta>1$, $\gamma>0$, and $\kappa,k>0$. Gelation th…

Consider coagulating Brownian particles in dimension $d\geq 3$, with particle mass $m$ and radius related by $r=m^{\chi}$. Assume that the diffusion coefficients…