Unboundedness for solutions to a degenerate drift-diffusion equation with the \(L^{1}\)-supercritical and the energy subcritical exponent

DOI10.1016/j.jmaa.2017.12.040zbMath1390.35026OpenAlexW2776100834MaRDI QIDQ1706568

Hiroshi Wakui

Publication date: 22 March 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.12.040

zbMATH Keywords

scaling invarianceHardy-Littlewood-Sobolev inequalityPatlak-Keller-Segel systemSmoluchowski-Poisson modelsvirial law

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Degenerate parabolic equations (35K65) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44) Quasilinear parabolic equations (35K59)

Cites Work

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• Blowup of solutions to generalized Keller-Segel model
• Free energy and self-interacting particles
• Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems.
• Degenerate parabolic equation with critical exponent derived from the kinetic theory. II: Blowup threshold.
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Initiation of slime mold aggregation viewed as an instability
• Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
• Degenerate parabolic equation with critical exponent derived from the kinetic theory: I: Generation of the weak solution
• On a nonlinear elliptic equation arising in a free boundary problem
• Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type.
• Threshold of global behavior of solutions to a degenerate drift-diffusion system in between two critical exponents
• The degenerate drift-diffusion system with the Sobolev critical exponent
• Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
• Global Existence of Solutions to a Parabolic-Elliptic System of Drift-Diffusion Type in <b><i>R</i></b>²
• Non-uniform bound and finite time blow up for solutions to a drift–diffusion equation in higher dimensions
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• The Debye system: existence and large time behavior of solutions
• Global existence of solutions to a parabolic system for chemotaxis in two space dimensions
• Fluid mechanical approximation to the degenerated drift-diffusion system from the compressible Navier-Stokes-Poisson system
• An Initial Value Problem from Semiconductor Device Theory
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains