Finite-Time Singularities of an Aggregation Equation in $${\mathbb {R}^n}$$ with Fractional Dissipation

By Dong Li, José L. Rodrigo. 2009

52 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/68f1f3126e93714556f8a737a68928160acffb8c

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In Applied Mathematics

In Modeling and Simulation

In Public Health, Environmental and Occupational Health

Citations in the corpus

Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion (2010, background): “Some recent work on this problem includes [5, 3, 4] for the inviscid case [26, 25, 24] for the problem with fractional diffusion and [27] for the problem in 1D with nonlinear diffusion.”
Exploding solutions for a nonlocal quadratic evolution problem (2010, background): “We refer the interested reader to [1, 12, 15, 16, 17, 18, 19, 21] where other equations with fractal type diffusion have been considered.”
Refined blowup criteria and nonsymmetric blowup of an aggregation equation (2009, background): “( 25 )). In the subcritical case the a priori L1x conservation allows us”
Blow-up in multidimensional aggregation equations with mildly singular interaction kernels (2009, result): “Equation (1.1) with additional fractional diusion also has some prior and recent study in the literature, namely [7, 24 , 25].”
Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion (2010, background): “also [31, 26, 19] for parabolic-parabolic Keller-Segel systems. For the inviscid problem, see the recent works of [41, 5, 4, 6, 22]. For a study of these equations with fractional linear diﬀusion see [42, 43, 9]. When the diﬀusion is suﬃciently nonlinear and the kernel is in L1, (1) may be written a”
Finite-time blow-up of L∞-weak solutions of an aggregation equation (2010, background): “The model in [23] included degenerate density dependent diffusion and blow-up was not observed numerically, while [ 18 ] rigorously studied (1.1) with the addition of fractional linear diffusion.”
Lp theory for the multidimensional aggregation equation (2011, unknown): “The same equation with additional diusion has been considered in [7, 9, 13, 20, 27, 29 , 30, 32] although we do not consider that case in this paper.”