### Impacto

### Downloads

Downloads per month over past year

Herrero, Miguel A. and Velázquez, J.J. L.
(1990)
*Asymptotic properties of a semilinear heat equation with strong absorption and small diffusion.*
Mathematische Annalen, 288
(4).
pp. 675-695.
ISSN 0025-5831

PDF
Restringido a Repository staff only 893kB |

Official URL: http://www.springerlink.com/content/r7plvk7500318562/

## Abstract

In this paper the authors study the asymptotic behaviour of solutions uε(x,t) of the Cauchy problems as ε goes to zero: ut−εΔu+up=0, x∈RN, t>0; u(x,0)=u0(x), x∈RN, 0<p<1. Compared with the explicit solution u¯(x,t) and the extinction time T0E(x) of the corresponding spatially independent initial value problem: ut+up=0, x∈RN, t>0; u(x,0)=u0(x), x∈RN, it is proved under certain assumptions that uε(x,t)→u¯(x,t) as ε↓0 uniformly on compact subsets of RN ×[0,∞) and, moreover, a precise estimate is given. Local and global estimates for extinction time are also given. The proofs are somewhat technical

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Blow-up time; parabolic equations; variational inequalities; thermal waves; support; semilinear heat equation; strong absorption; small diffusion; Cauchy problems; convergence; extinction times |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 18093 |

Deposited On: | 31 Jan 2013 09:10 |

Last Modified: | 12 Dec 2018 15:08 |

### Origin of downloads

Repository Staff Only: item control page