Global existence vs. blowup for the one dimensional quasilinear Smoluchowski-Poisson system
classification
🧮 math.AP
keywords
blowupdimensionalmassquasilinearsmoluchowski-poissonsolutionscoefficientcritical
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We prove that, unlike in several space dimensions, there is no critical (nonlinear) diffusion coefficient for which solutions to the one dimensional quasilinear Smoluchowski-Poisson equation with small mass exist globally while finite time blowup could occur for solutions with large mass.
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