Nonlinear Diffusion with Fractional Laplacian Operators

By Juan Luis V'azquez. 2012

223 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d10e0b9bb18c070711f99052ac8d0bab7850268e

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Hitchhiker's guide to the fractional Sobolev spaces (2011, background): “equations, are now experiencing impressive applications in different subjects, such as, among others, the thin obstacle problem [87, 69], optimization [37], finance [26], phase transitions [2, 14, 88, 40, 45], stratified materials [83, 23, 24], anomalous diffusion [68, 98, 65], crystal dislocation [”
On the Evolutionary Fractional p-Laplacian (2015, background): “1), is hence the nonlinear pendant to the fractional regional Laplacian mentioned above and appears, for instance, as a type of nonlinear diffusion, see [34].”
Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domains (2014, unknown): “…de Cantoblanco, 28049 Madrid, Spain (b) e-mail address: matteo.bonforte@uam.es (c) Université Aix-Marseille, I2M, Centre de Mathématique et Informatique, Technopôle de ChateauGiombert, Marseille, France (d) e-mail address: sire@cmi.univ-mrs.fr (e) e-mail address: juanluis.vazquez@uam.es Contents”
Local Elliptic Regularity for the Dirichlet Fractional Laplacian (2017, unknown): “Among others, we mention applications in elasticity [8], turbulence [2], anomalous transport and diffusion [5, 21], porousmedia flow [32], image processing [14], wave propagation in heterogeneous high contrastmedia [33].”
A General Fractional Porous Medium Equation (2011, background): “A more detailed discussion on these issues is contained in the survey paper [40].”
Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity (2014, background): “1) relies not only on mathematical purposes but also on their significance in real models, as explained by Caffarelli in [9]–[11], and by Vázquez in [30]–[31]; see also [14].”
Recent progress in the theory of Nonlinear Diffusion with Fractional Laplacian Operators (2014, methodology): “equations involving nonlocal, long-range diffusion effects.”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, background): “All this is carefully explained in [245].”