Hendrik J. Kuiper
We consider the problem
with nonnegative, nontrivial, continuous initial condition,
An integral inequality is obtained that can be used to find an exponent such that this problem has no nontrivial global solution when . This integral inequality may also be used to estimate the maximal such that there is a solution for . This is illustrated for the case and with initial condition , , by obtaining a bound of the form .
Submitted May 15, 2003. Published June 13, 2003.
Math Subject Classifications: 35K55, 35B33, 35B30.
Key Words: Nonlinear parabolic equation, blow-up, lifespan, critical exponent.
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| Hendrik J. Kuiper |
Department of Mathematics
Arizona State University
Tempe, AZ 85287-1804 USA
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