convection, diffusion, superquadratic, nonlinearity
A nonlinear convection-diffusion equation with boundary conditions that conserve the spatial integral of the solution is considered. Previous results on nite-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 suffcient to imply that a large class of nonnegative solutions blow up in nite time.
Original Publication Citation
Proceedings of the American Mathematical Society, Vol 129, no 11, pp 3353-3362.
BYU ScholarsArchive Citation
Fisher, Todd L. and Grant, Christopher P., "Blowup in a Mass-Conserving Convection-Diffusion Equation with Superquadratic Nonlinearity" (2001). All Faculty Publications. 576.
First published in Proceedings of the American Mathematical Society Vol 129, no 11 by The American Mathematical Society
Physical and Mathematical Sciences
© 2001 The American Mathematical Society
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