Space-time fractional diffusion on bounded domains
By Zhen-Qing Chen, Mark M. Meerschaert, Erkan Nane. 2011
143 citations recorded by the source corpus.
Abstract Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space–time fractional diffusion equations on bounded domains, as well as probabilistic representations of these solutions, which are useful for particle tracking codes.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/c1ad1065ca3c0149069fd228af5325ad1f6be9b0
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Suleyman Ulusoy
- Erkan Nane
- Mark M. Meerschaert
- Zhiping Mao
- Mark Ainsworth
- Ngartelbaye Guerngar
- Xiaoning Zheng
- G. Em Karniadakis
In Modeling and Simulation
- G. Em Karniadakis
- Suleyman Ulusoy
- Zhiping Mao
- Erkan Nane
- Guofei Pang
- Mark Ainsworth
- Mark M. Meerschaert
- Fangying Song
In Numerical Analysis
- Suleyman Ulusoy
- G. Em Karniadakis
- Ngartelbaye Guerngar
- Mark Ainsworth
- Zhiping Mao
- Fangying Song
- Mark M. Meerschaert
- Guofei Pang
Citations in the corpus
- What is the fractional Laplacian? A comparative review with new results (2018, background): “A nice proof of this equivalence can be found in [79], Lemma 4.”
- Inverse problem for a three-parameter space-time fractional diffusion equation (2018, background): “Following [6], a weak solution of Problem (2.”
- A UNIQUENESS RESULT FOR AN INVERSE PROBLEM IN A SPACE-TIME FRACTIONAL DIFFUSION EQUATION (2013, methodology): “n=1 λ n 〈f, ψn〉(2) <∞, for some k that satisfies the following inequality (see [1, 3] for details): k > −1 + 7 2α .”