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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Todd L. Fisher and Christopher P. Grant
Journal: Proc. Amer. Math. Soc. 129 (2001), 3353-3362
MSC (1991): Primary 35B30, 35B40, 35K20, 35K60
Published electronically: April 9, 2001
MathSciNet review: 1845013
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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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Additional Information

Todd L. Fisher
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730
Email: tfisher@math.nwu.edu

Christopher P. Grant
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: grant@math.byu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05992-5
PII: S 0002-9939(01)05992-5
Received by editor(s): March 23, 2000
Published electronically: April 9, 2001
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2001 American Mathematical Society