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Paper
IPM / M / 179 |
School of Mathematics
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Title: |
On the spectral properties of generalized non self-adjoint elliptic systems of differential operators degenerated on the boundary of domain
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Author(s): |
| 1. |
A. Sameripour
| | 2. |
K. Seddighi
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Status: |
Published
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Journal: |
Bull. Iranian Math. Soc.
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No.: |
1
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Vol.: |
24
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Year: |
1998
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Pages: |
15-32
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Supported by: |
IPM
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Abstract: |
Let Ω ⊂ Rn be a bounded domain with smooth boundary
i.e. ∂Ω ∈ C∞. In this paper we consider
the non-selfadjoint operator A on the space
Hl=L2(Ω)l=L2(Ω)l ×…×L2(Ω)
(l-times) associated with the noncoercive bilinear form
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A[u,v]= | ⌠
⌡
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Ω
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〈ρα (x) a(x) q(x) Di u (x), ρα (x) Dj u(x)〉Cl dx, |
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where D[A]=W°2,αn(Ω)l is the domain of the bilinear form associated
with the operator A defined by
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(Au)(x)= |
n
∑
i,j=1
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(−1)jDj (ρ2α (x) aij (x)q(x) Di u(x)), |
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with the
Dirichlet-type boundary conditions, here ρ(x)=dist{x,∂Ω}, 0 ≤ α < 1, aij(x) ∈ C2(―Ω), aij=―aji, |s| ≤ MΣi,j=1n aij (x) si―sj (x ∈ Ω, s ∈ Cn), the matrix q(x) has distinct eigenvalues
contained in the sector Φ = {z ∈ C:|argz| ≤ φ}, φ ∈ (0,π).
We will find the resolvent and some other spectral properties of
A.
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