Asymptotic behaviour of solutions to the coagulation–fragmentation equations. I. The strong fragmentation case

DOI10.1017/S0308210500027888zbMath0760.34044OpenAlexW1978247241MaRDI QIDQ4030478

Jack Carr

Publication date: 1 April 1993

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500027888

zbMATH Keywords

asymptotic behaviourdiscrete coagulation-fragmentation equationstime-evolution of cluster growth

Mathematics Subject Classification ID

Statistical mechanics of polymers (82D60) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (29)

Trend to Equilibrium for the Coagulation-Fragmentation Equation ⋮ The discrete diffusive coagulation-fragmentation equations with scattering ⋮ Smoothness of moments of the solutions of discrete coagulation equations with diffusion ⋮ Asymptotic behaviour of solutions to the Becker-Döring equations ⋮ Boltzmann and Poincaré entropy, Boltzmann extremals, and Hamilton-Jacobi method for non-Hamiltonian situation ⋮ Proof of dynamical scaling in Smoluchowski's coagulation equation with constant kernel ⋮ An introduction to mathematical models of coagulation--fragmentation processes: a discrete deterministic mean-field approach ⋮ Asymptotic behavior of solutions to the coagulation-fragmentation equations. II: Weak fragmentation ⋮ Finite-dimensional coagulation-fragmentation dynamics ⋮ Trend to equilibrium for the Becker-Döring equations : an analogue of Cercignani's conjecture ⋮ Mass-conserving solutions to coagulation-fragmentation equations with nonintegrable fragment distribution function ⋮ Existence and uniqueness of steady-state solution to a singular coagulation-fragmentation equation ⋮ Global classical solutions of coagulation-fragmentation equations with unbounded coagulation rates ⋮ A note on the discrete coagulation equations with collisional breakage ⋮ Convergence to equilibrium for the continuous coagulation-fragmentation equation ⋮ Applications of improved duality lemmas to the discrete coagulation-fragmentation equations with diffusion ⋮ Global solvability of a continuous model for nonlocal fragmentation dynamics in a moving medium ⋮ Asymptotic behaviour of solutions to the diffusive fragmentation-coagulation system ⋮ Analytic fragmentation semigroups and classical solutions to coagulation-fragmentation equations -- a survey ⋮ Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance ⋮ Generalized Boltzmann-type equations for aggregation in gases ⋮ Coagulation-fragmentation model for animal group-size statistics ⋮ Asymptotic behaviour of solutions to the generalized Becker–Döring equations for general initial data ⋮ Kinetics of cell surface capping ⋮ Smoluchowski's discrete coagulation equation with forcing ⋮ Fragmentation–diffusion model. Existence of solutions and their asymptotic behaviour ⋮ Stationary solutions to coagulation-fragmentation equations ⋮ On the existence of moments of solutions to fragmentation equations ⋮ Existence, Uniqueness and Mass Conservation for the Coagulation-Fragmentation Equation

Cites Work

• The discrete coagulation-fragmentation equations: existence, uniqueness, and density conservation.
• The Becker-Döring cluster equations: Basic properties and asymptotic behaviour of solutions
• Convergence to equilibrium in a system of reacting polymers
• Asymptotic behaviour of solutions to the Becker-Döring equations for arbitrary initial data

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