Details
| Original language | English |
|---|---|
| Pages (from-to) | 31-45 |
| Number of pages | 15 |
| Journal | Archiv der Mathematik |
| Volume | 71 |
| Issue number | 1 |
| Publication status | Published - 2 Jul 1998 |
| Externally published | Yes |
Abstract
We consider semilinear parabolic equations on unbounded domains in ℝ2 or ℝ3 with forcing polynomial nonlinearities of the form g(u) = aup + bup+1 + ⋯ with a > 0 and p ≧ 2. It is shown that the zero solution of the induced semiflow is positively unstable, provided p = 2 and the domain contains arbitrarily large spheres. If p > 2 and if g possesses a positive root, then the zero solution is positively stable.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Archiv der Mathematik, Vol. 71, No. 1, 02.07.1998, p. 31-45.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stability properties of parabolic equations in unbounded domains
AU - Escher, Joachim
AU - Scarpellini, Bruno
PY - 1998/7/2
Y1 - 1998/7/2
N2 - We consider semilinear parabolic equations on unbounded domains in ℝ2 or ℝ3 with forcing polynomial nonlinearities of the form g(u) = aup + bup+1 + ⋯ with a > 0 and p ≧ 2. It is shown that the zero solution of the induced semiflow is positively unstable, provided p = 2 and the domain contains arbitrarily large spheres. If p > 2 and if g possesses a positive root, then the zero solution is positively stable.
AB - We consider semilinear parabolic equations on unbounded domains in ℝ2 or ℝ3 with forcing polynomial nonlinearities of the form g(u) = aup + bup+1 + ⋯ with a > 0 and p ≧ 2. It is shown that the zero solution of the induced semiflow is positively unstable, provided p = 2 and the domain contains arbitrarily large spheres. If p > 2 and if g possesses a positive root, then the zero solution is positively stable.
UR - http://www.scopus.com/inward/record.url?scp=0032397002&partnerID=8YFLogxK
U2 - 10.1007/s000130050231
DO - 10.1007/s000130050231
M3 - Article
AN - SCOPUS:0032397002
VL - 71
SP - 31
EP - 45
JO - Archiv der Mathematik
JF - Archiv der Mathematik
SN - 0003-889X
IS - 1
ER -