Blowup in a mass-conserving convection-diffusion equation with superquadratic nonlinearity

Fisher, Todd; Grant, Christopher

doi:10.1090/S0002-9939-01-05992-5

Blowup in a mass-conserving convection-diffusion equation with superquadratic nonlinearity
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by Todd L. Fisher and Christopher P. Grant PDF

Proc. Amer. Math. Soc. 129 (2001), 3353-3362 Request permission

Abstract:

A nonlinear convection-diffusion equation with boundary conditions that conserve the spatial integral of the solution is considered. Previous results on finite-time blowup of solutions and on decay of solutions to the corresponding Cauchy problem were based on the assumption that the nonlinearity obeyed a power law. In this paper, it is shown that assumptions on the growth rate of the nonlinearity, which take the form of weak superquadraticity and strong superlinearity criteria, are sufficient to imply that a large class of nonnegative solutions blow up in finite time.

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