ArticleProceedings. Mathematical, physical, and engineering sciences2019
Extensions and solutions for nonlinear diffusion equations and random walks.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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Who cites it
2 citing papers in PubMed.
- Results for Nonlinear Diffusion Equations with Stochastic Resetting.Entropy (Basel, Switzerland) · 2023Article
- Nonlinear Fokker-Planck Equations, H-Theorem and Generalized Entropy of a Composed System.Entropy (Basel, Switzerland) · 2023Article
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Authors and funding
4 authors.
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Abstract
We investigate a connection between random walks and nonlinear diffusion equations within the framework proposed by Einstein to explain the Brownian motion. We show here how to properly modify that framework in order to handle different physical scenarios. We obtain solutions for nonlinear diffusion equations that emerge from the random walk approach and analyse possible connections with a generalized thermostatistics formalism. Finally, we conclude that fractal and fractional derivatives may emerge in the context of nonlinear diffusion equations, depending on the choice of distribution functions related to the spreading of systems.
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