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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Cite this
Asymptotic behavior of solutions for a system of semilinear heat equations and the corresponding damped wave system. / Nishihara, Kenji.
In: Osaka Journal of Mathematics, Vol. 49, No. 2, 06.2012, p. 331-348.Research output: Contribution to journal › Article
}
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
AN - SCOPUS:84863482066
VL - 49
SP - 331
EP - 348
JO - Osaka Journal of Mathematics
JF - Osaka Journal of Mathematics
SN - 0030-6126
IS - 2
ER -