### Abstract

Consider the Cauchy problem for a system of weakly coupled heat equations, whose typical one is p= with p, q ≥ 1, pq > 1. When p, q satisfy max ((p+1)/(pq - 1), (q + 1)/(pq -1)) < N/2, the exponents p, q are supercritical. In this paper we assort the supercritical exponent case to two cases. In one case both p and q are bigger than the Fujita exponent ρF (N) = 1+2/N, while in the other case ρF (N) is between p and q. In both cases we obtain the time-global and unique existence of solutions for small data and their asymptotic behaviors. These observation will be applied to the corresponding system of the damped wave equations in low dimensional space.

Original language | English |
---|---|

Pages (from-to) | 331-348 |

Number of pages | 18 |

Journal | Osaka Journal of Mathematics |

Volume | 49 |

Issue number | 2 |

Publication status | Published - 2012 Jun |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Osaka Journal of Mathematics*,

*49*(2), 331-348.

**Asymptotic behavior of solutions for a system of semilinear heat equations and the corresponding damped wave system.** / Nishihara, Kenji.

Research output: Contribution to journal › Article

*Osaka Journal of Mathematics*, vol. 49, no. 2, pp. 331-348.

}

TY - JOUR

T1 - Asymptotic behavior of solutions for a system of semilinear heat equations and the corresponding damped wave system

AU - Nishihara, Kenji

PY - 2012/6

Y1 - 2012/6

N2 - Consider the Cauchy problem for a system of weakly coupled heat equations, whose typical one is p= with p, q ≥ 1, pq > 1. When p, q satisfy max ((p+1)/(pq - 1), (q + 1)/(pq -1)) < N/2, the exponents p, q are supercritical. In this paper we assort the supercritical exponent case to two cases. In one case both p and q are bigger than the Fujita exponent ρF (N) = 1+2/N, while in the other case ρF (N) is between p and q. In both cases we obtain the time-global and unique existence of solutions for small data and their asymptotic behaviors. These observation will be applied to the corresponding system of the damped wave equations in low dimensional space.

AB - Consider the Cauchy problem for a system of weakly coupled heat equations, whose typical one is p= with p, q ≥ 1, pq > 1. When p, q satisfy max ((p+1)/(pq - 1), (q + 1)/(pq -1)) < N/2, the exponents p, q are supercritical. In this paper we assort the supercritical exponent case to two cases. In one case both p and q are bigger than the Fujita exponent ρF (N) = 1+2/N, while in the other case ρF (N) is between p and q. In both cases we obtain the time-global and unique existence of solutions for small data and their asymptotic behaviors. These observation will be applied to the corresponding system of the damped wave equations in low dimensional space.

UR - http://www.scopus.com/inward/record.url?scp=84863482066&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863482066&partnerID=8YFLogxK

M3 - Article

VL - 49

SP - 331

EP - 348

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 2

ER -