Self-similar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels

DOI10.1016/j.anihpc.2015.04.002zbMath1357.35073arXiv1411.1602OpenAlexW2964007175MaRDI QIDQ327753

Sebastian Throm, Barbara Niethammer, Juan J. L. Velazquez

Publication date: 19 October 2016

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.1602

zbMATH Keywords

compactness argumentfat tail profileregularized problemslow decay

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Integro-partial differential equations (45K05) Interacting particle systems in time-dependent statistical mechanics (82C22) Positive solutions of integral equations (45M20) Self-similar solutions to PDEs (35C06) Integro-partial differential equations (35R09)

Related Items (16)

Mathematical theory of exchange-driven growth ⋮ On self-similar solutions to a kinetic equation arising in weak turbulence theory for the nonlinear Schrödinger equation ⋮ Self-similar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels ⋮ Non-equilibrium stationary solutions for multicomponent coagulation systems with injection ⋮ Calculus of variations. Abstracts from the workshop held August 14--20, 2022 ⋮ Homoenergetic solutions of the Boltzmann equation: the case of simple-shear deformations ⋮ The scaling hypothesis for Smoluchowski's coagulation equation with bounded perturbations of the constant kernel ⋮ Self-similar profiles for homoenergetic solutions of the Boltzmann equation: particle velocity distribution and entropy ⋮ Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel ⋮ Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity one ⋮ Self-similar asymptotic behavior for the solutions of a linear coagulation equation ⋮ Tail behaviour of self-similar profiles with infinite mass for Smoluchowski's coagulation equation ⋮ Stability and uniqueness of self-similar profiles in \(L^1\) spaces for perturbations of the constant kernel in Smoluchowski's coagulation equation ⋮ Stationary non-equilibrium solutions for coagulation systems ⋮ Uniqueness of fat-tailed self-similar profiles to Smoluchowski’s coagulation equation for a perturbation of the constant kernel ⋮ Self-similar spreading in a merging-splitting model of animal group size

Cites Work

• Self-similar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels
• Self-similar solutions with fat tails for a coagulation equation with diagonal kernel
• On the Boltzmann equation for diffusively excited granular media
• Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists
• On self-similarity and stationary problem for fragmentation and coagulation models.
• Self-similar solutions with fat tails for Smoluchowski's coagulation equation with locally bounded kernels
• Dust and self-similarity for the Smoluchowski coagulation equation
• Existence of self-similar solutions to Smoluchowski's coagulation equation
• Approach to self‐similarity in Smoluchowski's coagulation equations
• Local properties of self-similar solutions to Smoluchowski’s coagulation equation with sum kernels

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