Finite-time blow-up for solutions to a degenerate drift-diffusion equation for a fast-diffusion case

DOI10.1088/1361-6544/ab0069zbMath1411.35153OpenAlexW2944013758WikidataQ127941431 ScholiaQ127941431MaRDI QIDQ5742473

Publication date: 14 May 2019

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/ab0069

zbMATH Keywords

existence of weak solution free energy finite-time blow-up Shannon's inequality virial law degenerate drift-diffusion system

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) Quasilinear parabolic equations (35K59)

Related Items (2)

Shannon's inequality for the Rényi entropy and an application to the uncertainty principle ⋮ Asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case

Cites Work

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A note on the free energy of the Keller-Segel model for subcritical and supercritical cases
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.
Extinction, decay and blow-up for Keller-Segel systems of fast diffusion type
Asymptotic stability of a decaying solution to the Keller-Segel system of degenerate type.
Degenerate parabolic equation with critical exponent derived from the kinetic theory. II: Blowup threshold.
Initiation of slime mold aggregation viewed as an instability
Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
Blowup in infinite time of radial solutions for a parabolic-elliptic system in high-dimensional Euclidean spaces
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
Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type.
Long time behavior of solutions of Nernst-Planck and Debye-Hückel drift-diffusion systems
Existence and blowing up for a system of the drift-diffusion equation in $R^2$.
Finite time blow up and non-uniform bound for solutions to a degenerate drift-diffusion equation with the mass critical exponent under non-weight condition
The degenerate drift-diffusion system with the Sobolev critical exponent
Asymptotic behavior for critical Patlak-Keller-Segel model and a repulsive-attractive aggregation equation
Non-isothermal Smoluchowski-Poisson equations as a singular limit of the Navier-Stokes-Fourier-Poisson system
Well-posedness for the drift-diffusion system in $L^p$ arising from the semiconductor device simulation
Global Existence of Solutions to a Parabolic-Elliptic System of Drift-Diffusion Type in R2
The Patlak–Keller–Segel Model and Its Variations: Properties of Solutions via Maximum Principle
Multidimensional Degenerate Keller–Segel System with Critical Diffusion Exponent $2n/(n+2)$
Non-uniform bound and finite time blow up for solutions to a drift–diffusion equation in higher dimensions
Finite-time blow-up in a quasilinear system of chemotaxis
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
Existence and nonexistence of solutions for a model of gravitational interaction of particles, III
Large Mass Global Solutions for a Class ofL¹-Critical Nonlocal Aggregation Equations and Parabolic-Elliptic Patlak-Keller-Segel Models
Fluid mechanical approximation to the degenerated drift-diffusion system from the compressible Navier-Stokes-Poisson system
Chemotactic collapse in a parabolic system of mathematical biology
Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains

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