Global Stability and Bounds for Coarsening Rates Within the Mean-Field Theory for Domain Coarsening

DOI10.1080/03605300500481533zbMath1113.35029OpenAlexW2088115309MaRDI QIDQ3424261

Juan J. L. Velazquez, Barbara Niethammer

Publication date: 15 February 2007

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://eprints.ucm.es/id/eprint/12431/1/2005global-20.pdf

zbMATH Keywords

convergenceself-similarityLifshitz-Slyozov-Wagner equationbounds on coarsening ratesLSW equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Integro-partial differential equations (45K05) First-order nonlinear hyperbolic equations (35L60) Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics (82C21) Asymptotics of solutions to integral equations (45M05)

Related Items (6)

Transient and self-similar dynamics in thin film coarsening ⋮ On global stability for Lifschitz-Slyozov-Wagner like equations ⋮ Self-similar behaviour for noncompactly supported solutions of the LSW model ⋮ Bounds on coarsening rates for the Lifschitz-Slyozov-Wagner equation ⋮ On global asymptotic stability for the LSW model with subcritical initial data ⋮ Global stability for a class of nonlinear PDE with non-local term

Cites Work

• Non-self-similar behavior in the LSW theory of Ostwald ripening
• A numerical study on large-time asymptotics of the Lifshitz--Slyozov system
• Coarsening rates for models of multicomponent phase separation
• Asymptotic behaviour of solutions to a simplified Lifshitz-Slyozov equation
• Upper bounds on coarsening rates
• An upper bound on the coarsening rate for mushy zones in a phase field model
• Well-posedness for measure transport in a family of nonlocal domain coarsening models
• On the Initial-Value Problem in the Lifshitz--Slyozov--Wagner Theory of Ostwald Ripening
• Universal Bounds on Coarsening Rates for Mean-Field Models of Phase Transitions
• On the convergence to the smooth self-similar solution in the LSW model
• The LSW model for domain coarsening: Asymptotic behavior for conserved total mass.

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