Details
| Original language | English |
|---|---|
| Pages (from-to) | 325-352 |
| Number of pages | 28 |
| Journal | Analysis (Germany) |
| Volume | 20 |
| Issue number | 4 |
| Publication status | Published - 12 Jan 2000 |
Abstract
A suitable reduction of elliptic equations with nonlinear dynamic boundary conditions leads to seinilinear evolution equations on the boundary involving first order elliptic pseudo-differential operators. In case of unbounded boundaries the spectra of these operators in general contain 0 as a cluster point, and therefore the principle of linearized stability is not accessible. For a suitable class of polynomial nonlinearities a criterion is provided ensuring the H1-stability of the zero solution in space dimensions N = 2 and N = 3 with respect to positive H1-σ-perturbations. where σ = t(N – 2) for some r > 0. Applications to a particular geometrical configuration are also discussed.
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Applied Mathematics
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In: Analysis (Germany), Vol. 20, No. 4, 12.01.2000, p. 325-352.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stable Equilibria to Elliptic Equations in Unbounded Domains with Nonlinear Dynamic Boundary Conditions
AU - Escher, Joachim
PY - 2000/1/12
Y1 - 2000/1/12
N2 - A suitable reduction of elliptic equations with nonlinear dynamic boundary conditions leads to seinilinear evolution equations on the boundary involving first order elliptic pseudo-differential operators. In case of unbounded boundaries the spectra of these operators in general contain 0 as a cluster point, and therefore the principle of linearized stability is not accessible. For a suitable class of polynomial nonlinearities a criterion is provided ensuring the H1-stability of the zero solution in space dimensions N = 2 and N = 3 with respect to positive H1-σ-perturbations. where σ = t(N – 2) for some r > 0. Applications to a particular geometrical configuration are also discussed.
AB - A suitable reduction of elliptic equations with nonlinear dynamic boundary conditions leads to seinilinear evolution equations on the boundary involving first order elliptic pseudo-differential operators. In case of unbounded boundaries the spectra of these operators in general contain 0 as a cluster point, and therefore the principle of linearized stability is not accessible. For a suitable class of polynomial nonlinearities a criterion is provided ensuring the H1-stability of the zero solution in space dimensions N = 2 and N = 3 with respect to positive H1-σ-perturbations. where σ = t(N – 2) for some r > 0. Applications to a particular geometrical configuration are also discussed.
UR - http://www.scopus.com/inward/record.url?scp=2442704885&partnerID=8YFLogxK
U2 - 10.1524/anly.2000.20.4.325
DO - 10.1524/anly.2000.20.4.325
M3 - Article
AN - SCOPUS:2442704885
VL - 20
SP - 325
EP - 352
JO - Analysis (Germany)
JF - Analysis (Germany)
SN - 0174-4747
IS - 4
ER -