Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws

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Blowup of solutions to generalized Keller–Segel model (2008, background): “2], [8,9]) which permits us to control locally the nonlinearity in (1.”
Entropy formulation for fractal conservation laws (2007, background): “Most of the studies (well-posedness, asymptotic behaviour, etc) are concerned with the range of exponent λ ∈]1, 2] (see [1, 2 , 7, 6, 8, 10]).”
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 [”
From the long jump random walk to the fractional Laplacian (2009, background): “Indeed, nonlocal operators arise in the thin obstacle problem [Caf79], in optimization [DL76], in finance [CT04], in phase transitions [AB98, ABS98, CSM05, SV08b], in stratified materials [SV08a], in anomalous diffusion [MK00], in crystal dislocation [Tol97], in soft thin films [Kur06], in some mode”
Asymptotics for conservation laws involving Levy diffusion generators (2001, background): “A detailed discussion of this issue for the general problem (1.1)–(1.3) will appear elsewhere, cf. [ 6 ].”