### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Analysis

### Cite this

*Electronic Journal of Differential Equations*,

*2003*, 1-11.

**Life span of nonnegative solutions to certain quasilinear parabolic cauchy problems.** / Kuiper, Hendrik J.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Life span of nonnegative solutions to certain quasilinear parabolic cauchy problems

AU - Kuiper, Hendrik J.

PY - 2003/6/13

Y1 - 2003/6/13

N2 - 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.

AB - 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.

KW - Blow-up

KW - Critical exponent

KW - Lifespan

KW - Nonlinear parabolic equation

UR - http://www.scopus.com/inward/record.url?scp=3042582256&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042582256&partnerID=8YFLogxK

M3 - Article

VL - 2003

SP - 1

EP - 11

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

SN - 1072-6691

ER -