Electron. J. Diff. Eqns., Vol. 2003(2003), No. 66, pp. 111.
Life span of nonnegative solutions to certain quasilinear
parabolic Cauchy problems
Hendrik J. Kuiper
Abstract:
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, blowup, lifespan,
critical exponent.
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Hendrik J. Kuiper
Department of Mathematics
Arizona State University
Tempe, AZ 852871804 USA
email: kuiper@asu.edu 
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