抄録
We construct some particular kind of solution to the two - dimensional equivariant wave map problem with inhomogeneous source term in space-time domain of type Ωα(t) = (x ∈ ℝ2: |x| α < t), where α ∈ (0, 1]. More precisely, we take the initial data (u0, u1) at time T in the space H1+ε × Hε with some ε > 0. The source term is in L1((0, T);Hε (Ωα(t))) and we show that the H1+ε - norm of the solution blows-up, when t → 0+ and α ∈ (0, 1-ε).
| 元の言語 | English |
|---|---|
| ページ（範囲） | 195-235 |
| ページ数 | 41 |
| ジャーナル | Rendiconti dell'Istituto di Matematica dell'Universita di Trieste |
| 巻 | 35 |
| 出版物ステータス | Published - 2003 1 1 |
| 外部発表 | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
これを引用
Concentration of local energy for two-dimensional wave maps. / Gueorguiev, Vladimir Simeonov; Ivanov, Angel.
：: Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, 巻 35, 01.01.2003, p. 195-235.研究成果: Article
}
TY - JOUR
T1 - Concentration of local energy for two-dimensional wave maps
AU - Gueorguiev, Vladimir Simeonov
AU - Ivanov, Angel
PY - 2003/1/1
Y1 - 2003/1/1
N2 - We construct some particular kind of solution to the two - dimensional equivariant wave map problem with inhomogeneous source term in space-time domain of type Ωα(t) = (x ∈ ℝ2: |x| α < t), where α ∈ (0, 1]. More precisely, we take the initial data (u0, u1) at time T in the space H1+ε × Hε with some ε > 0. The source term is in L1((0, T);Hε (Ωα(t))) and we show that the H1+ε - norm of the solution blows-up, when t → 0+ and α ∈ (0, 1-ε).
AB - We construct some particular kind of solution to the two - dimensional equivariant wave map problem with inhomogeneous source term in space-time domain of type Ωα(t) = (x ∈ ℝ2: |x| α < t), where α ∈ (0, 1]. More precisely, we take the initial data (u0, u1) at time T in the space H1+ε × Hε with some ε > 0. The source term is in L1((0, T);Hε (Ωα(t))) and we show that the H1+ε - norm of the solution blows-up, when t → 0+ and α ∈ (0, 1-ε).
KW - Blow-up of solution
KW - Equivariant wave maps
KW - H-spaces
UR - http://www.scopus.com/inward/record.url?scp=84964829185&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84964829185&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84964829185
VL - 35
SP - 195
EP - 235
JO - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste
JF - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste
SN - 0049-4704
ER -