We consider the problem (formula presented) with nonnegative, nontrivial, continuous initial condition, (formula presented) An integral inequality is obtained that can be used to find an exponent pc such that this problem has no nontrivial global solution when p ≤ pc. This integral inequality may also be used to estimate the maximal T > 0 such that there is a solution for 0 ≤ t < T. This is illustrated for the case ρ ≡ 1 and h ≡ 1 with initial condition u(x, 0) = σu0(x), σ > 0, by obtaining a bound of the form T ≤ C0σ-θ.
|Original language||English (US)|
|Number of pages||11|
|Journal||Electronic Journal of Differential Equations|
|State||Published - Jun 13 2003|
- Critical exponent
- Nonlinear parabolic equation
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