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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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Additional Information
  • Todd L. Fisher
  • Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730
  • MR Author ID: 681585
  • Email: tfisher@math.nwu.edu
  • Christopher P. Grant
  • Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
  • Email: grant@math.byu.edu
  • Received by editor(s): March 23, 2000
  • Published electronically: April 9, 2001
  • Communicated by: David S. Tartakoff
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3353-3362
  • MSC (1991): Primary 35B30, 35B40, 35K20, 35K60
  • DOI: https://doi.org/10.1090/S0002-9939-01-05992-5
  • MathSciNet review: 1845013