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

DOI:
https://doi.org/10.1090/S0002-9939-01-05992-5

Published electronically:
April 9, 2001

MathSciNet review:
1845013

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-01-05992-5

Received by editor(s):
March 23, 2000

Published electronically:
April 9, 2001

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2001
American Mathematical Society