Abstract
This paper is concerned with the study of the system of Laplace operators with perfect wall condition in the Lpframework. Our study includes a bounded domain, an exterior domain and a domain having noncompact boundary such as a perturbed half space. A direct application of our study is to prove the analyticity of the semigroup corresponding to the Maxwell equation of parabolic type, which appears as a linearized equation in the study of the nonstationary problem concerning the Ginzburg-Landau-Maxwell equation describing the Ginzburg-Landau model for superconductivity, the magnetohydrodynamic equation and the Navier-Stokes equation with Neumann boundary condition. And also, our theory is applicable to some solvability of the stationary problem of these nonlinear equations in the Lpframework.
| Original language | English |
|---|---|
| Pages (from-to) | 361-394 |
| Number of pages | 34 |
| Journal | Funkcialaj Ekvacioj |
| Volume | 47 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2004 Jan 1 |
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Keywords
- A system of Laplace operators
- Perfect wall condition
- Resolvent estimate
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology
Cite this
On a Resolvent Estimate of a System of Laplace Operators with Perfect Wall Condition. / Akiyama, T.; Shibata, Y.; Tsutsumi, M.; Kasai, H.
In: Funkcialaj Ekvacioj, Vol. 47, No. 3, 01.01.2004, p. 361-394.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On a Resolvent Estimate of a System of Laplace Operators with Perfect Wall Condition
AU - Akiyama, T.
AU - Shibata, Y.
AU - Tsutsumi, M.
AU - Kasai, H.
PY - 2004/1/1
Y1 - 2004/1/1
N2 - This paper is concerned with the study of the system of Laplace operators with perfect wall condition in the Lpframework. Our study includes a bounded domain, an exterior domain and a domain having noncompact boundary such as a perturbed half space. A direct application of our study is to prove the analyticity of the semigroup corresponding to the Maxwell equation of parabolic type, which appears as a linearized equation in the study of the nonstationary problem concerning the Ginzburg-Landau-Maxwell equation describing the Ginzburg-Landau model for superconductivity, the magnetohydrodynamic equation and the Navier-Stokes equation with Neumann boundary condition. And also, our theory is applicable to some solvability of the stationary problem of these nonlinear equations in the Lpframework.
AB - This paper is concerned with the study of the system of Laplace operators with perfect wall condition in the Lpframework. Our study includes a bounded domain, an exterior domain and a domain having noncompact boundary such as a perturbed half space. A direct application of our study is to prove the analyticity of the semigroup corresponding to the Maxwell equation of parabolic type, which appears as a linearized equation in the study of the nonstationary problem concerning the Ginzburg-Landau-Maxwell equation describing the Ginzburg-Landau model for superconductivity, the magnetohydrodynamic equation and the Navier-Stokes equation with Neumann boundary condition. And also, our theory is applicable to some solvability of the stationary problem of these nonlinear equations in the Lpframework.
KW - A system of Laplace operators
KW - Perfect wall condition
KW - Resolvent estimate
UR - http://www.scopus.com/inward/record.url?scp=33645446569&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33645446569&partnerID=8YFLogxK
U2 - 10.1619/fesi.47.361
DO - 10.1619/fesi.47.361
M3 - Article
AN - SCOPUS:33645446569
VL - 47
SP - 361
EP - 394
JO - Funkcialaj Ekvacioj
JF - Funkcialaj Ekvacioj
SN - 0532-8721
IS - 3
ER -