The diffusive limit of Carleman-type models in the range of very fast diffusion equations

DOI10.1007/s00028-009-0005-yzbMath1239.35070OpenAlexW2016616986MaRDI QIDQ423328

Giuseppe Toscani, Francesco Salvarani

Publication date: 2 June 2012

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-009-0005-y

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Nonlinear first-order PDEs (35F20) Self-similar solutions to PDEs (35C06)

Related Items (5)

A kinetic model for the formation of swarms with nonlinear interactions ⋮ Control of modeling errors in the coupling of linear transport and diffusion models ⋮ Diffusive limits of nonlinear hyperbolic systems with variable coefficients ⋮ Heterogeneous discrete kinetic model and its diffusion limit ⋮ ON A MACROSCOPIC LIMIT OF A KINETIC MODEL OF ALIGNMENT

Cites Work

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• The one-dimensional Darcy's law as the limit of a compressible Euler flow
• Nonexistence of solutions for nonlinear heat equations of fast-diffusion type
• Diffusive limit for finite velocity Boltzmann kinetic models
• The diffusive limit for Carleman-type kinetic models
• The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem
• Discrete Velocity Models of the Boltzmann Equation: A Survey on the Mathematical ASPECTS of the Theory
• A Nonlinear heat equation with singular diffusivity

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