Non-uniform bound and finite time blow up for solutions to a drift–diffusion equation in higher dimensions

DOI10.1142/S0219530515400060zbMath1331.35157OpenAlexW2179115940MaRDI QIDQ3466803

Hiroshi Wakui, Takayoshi Ogawa

Publication date: 25 January 2016

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

Full work available at URL: https://doi.org/10.1142/s0219530515400060

zbMATH Keywords

chemotaxisunbounded solutionfinite time blow-upcritical spacedrift-diffusion systemvirial functionalgeneralized Shannon inequality

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Initial value problems for second-order parabolic equations (35K15) Blow-up in context of PDEs (35B44)

Related Items (17)

Shannon's inequality for the Rényi entropy and an application to the uncertainty principle ⋮ Finite time blow up for a solution to system of the drift-diffusion equations in higher dimensions ⋮ Logarithmic Sobolev and Shannon's inequalities and an application to the uncertainty principle ⋮ Stability and instability of solutions to the drift-diffusion system ⋮ Global existence of solutions to the 4D attraction–repulsion chemotaxis system and applications of Brezis–Merle inequality ⋮ Singular limit problem for the Keller-Segel system and drift-diffusion system in scaling critical spaces ⋮ 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 ⋮ Finite time blow up and concentration phenomena for a solution to drift-diffusion equations in higher dimensions ⋮ Stable singularity formation for the Keller-Segel system in three dimensions ⋮ Unboundedness for solutions to a degenerate drift-diffusion equation with the \(L^{1}\)-supercritical and the energy subcritical exponent ⋮ Beckner type of the logarithmic Sobolev and a new type of Shannon’s inequalities and an application to the uncertainty principle ⋮ Finite-time blow-up for solutions to a degenerate drift-diffusion equation for a fast-diffusion case ⋮ The rate of concentration for the radially symmetric solution to a degenerate drift-diffusion equation with the mass critical exponent ⋮ Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions ⋮ Asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case ⋮ Maximal regularity and a singular limit problem for the Patlak-Keller-Segel system in the scaling critical space involving \textit{BMO} ⋮ Singular limit problem for the two-dimensional Keller-Segel system in scaling critical space

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