Interacting diffusions approximating the porous medium equation and propagation of chaos

DOI10.1016/j.spa.2006.09.003zbMath1263.60085OpenAlexW1987043692MaRDI QIDQ875911

Robert Philipowski

Publication date: 16 April 2007

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2006.09.003

zbMATH Keywords

porous medium equationpropagation of chaosinteracting diffusion processes

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Flows in porous media; filtration; seepage (76S05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) PDEs with randomness, stochastic partial differential equations (35R60)

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Cites Work

• Large systems of interacting particles and the porous medium equation
• Construction of diffusion processes associated with a porous medium equation
• Derivation of a porous medium equation from many Markovian particles and the propagation of chaos
• Propagation of chaos and fluctuations for a moderate model with smooth initial data
• A microscopic mechanism for the porous medium equation
• Probabilistic approximation for a porous medium equation.
• Simulation of the Solution of a Viscous Porous Medium Equation by a Particle Method
• A sequence of integro-differential equations approximating a viscous porous medium equation
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