The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion
By Juan Luis V'azquez. 2017
150 citations recorded by the source corpus.
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the last two centuries. It was followed by the theory of parabolic equations of different types. In a parallel development, the theory of stochastic partial differential equations gives a foundation to the probabilistic study of diffusion.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/342cacd3404245f8036f88ed5cc2b033c12596bf
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In Applied Mathematics
- Zhiping Mao
- Mark Ainsworth
- Xiaoning Zheng
- G. Em Karniadakis
- Fangying Song
- Christian Glusa
- Mark M. Meerschaert
- Anna Lischke
In Computational Theory and Mathematics
- G. Em Karniadakis
- Guofei Pang
- Wei Cai
- Xiaoning Zheng
- Mark Ainsworth
- Zhiping Mao
- Fangying Song
- Christian Glusa
In Modeling and Simulation
- G. Em Karniadakis
- Zhiping Mao
- Guofei Pang
- Mark Ainsworth
- Fangying Song
- Wei Cai
- Mamikon A. Gulian
- Mark M. Meerschaert
Citations in the corpus
- What is the fractional Laplacian? A comparative review with new results (2018, background): “Overview During the past few decades, scientists have been exploring fractional calculus as a tool for developing more sophisticated mathematical models that can accurately describe complex anomalous systems [1, 2, 3, 4].”