### Abstract

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 p_{c} such that this problem has no nontrivial global solution when p ≤ p_{c}. 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) = σu_{0}(x), σ > 0, by obtaining a bound of the form T ≤ C_{0}σ^{-θ}.

Original language | English (US) |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Electronic Journal of Differential Equations |

Volume | 2003 |

State | Published - Jun 13 2003 |

### Keywords

- Blow-up
- Critical exponent
- Lifespan
- Nonlinear parabolic equation

### ASJC Scopus subject areas

- Analysis

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## Cite this

Kuiper, H. J. (2003). Life span of nonnegative solutions to certain quasilinear parabolic cauchy problems.

*Electronic Journal of Differential Equations*,*2003*, 1-11.