Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type

By Masaki Kurokiba, T. Ogawa. Differential and Integral Equations, 2003

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The 8π‐problem for radially symmetric solutions of a chemotaxis model in the plane (2006, unknown): “For T > 0, it follows from (1.1) that IR(T )− IR(0) = − ∫ T 0 ∫ ∞ 0 ζR(s) ∂s ( 4s(M − 8π)s + M(M − 8π) 2π ) ds dt = − ∫ T 0 [ ζR(s) ( 4s(M − 8π)s + M(M − 8π) 2π )]∞ 0 dt + ∫ T 0 ∫ ∞ 0 ζ ′R(s) ( 4s(M − 8π)s + M(M − 8π) 2π ) ds dt .”
Well-posedness for the drift-diffusion system in Lp arising from the semiconductor device simulation (2008, methodology): “[16] M. Kurokiba, T. Ogawa, Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type, Differential Integral Equations 16 (4) (2003) 427–452.”
A Note on non-simultaneous blow-up for a drift-diffusion model (2010, methodology): “In this paper, it was shown that blow-up for the drift-diffusion model is also possible for a range of parameters, which was not considered in [3].”
Remarks on the blowup and global existence for a two species chemotactic Keller–Segel system in 2 (2011, methodology): “[15] Kurokiba, M. & Ogawa, T. (2003) Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type.”
The drift–diffusion system in two-dimensional critical Hardy space (2008, background): “(See [36].”