Regularity, local behavior and partial uniqueness for self-similar profiles of Smoluchowski's coagulation equation

DOI10.4171/RMI/653zbMath1242.82031arXiv0803.1462MaRDI QIDQ643325

José A. Cañizo, Stéphane Mischler

Publication date: 28 October 2011

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.1462

zbMATH Keywords

regularityasymptotic behavioruniquenessself-similaritycoagulation

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics (82C21) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05)

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Cites Work

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• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• 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.
• Proof of dynamical scaling in Smoluchowski's coagulation equation with constant kernel
• Scaling solutions of Smoluchowski's coagulation equation
• 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
• Dynamical Scaling in Smoluchowski's Coagulation Equations: Uniform Convergence
• Local properties of self-similar solutions to Smoluchowski’s coagulation equation with sum kernels
• Ordinary Differential Equations