Concentration of local energy for two-dimensional wave maps

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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);Hεα(t))) and we show that the H1+ε - norm of the solution blows-up, when t → 0+ and α ∈ (0, 1-ε).

Original languageEnglish
Pages (from-to)195-235
Number of pages41
JournalRendiconti dell'Istituto di Matematica dell'Universita di Trieste
Volume35
Publication statusPublished - 2003 Jan 1
Externally publishedYes

Fingerprint

Source Terms
Blow-up Solution
Energy
Equivariant
Space-time
Norm

Keywords

  • Blow-up of solution
  • Equivariant wave maps
  • H-spaces

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Concentration of local energy for two-dimensional wave maps. / Gueorguiev, Vladimir Simeonov; Ivanov, Angel.

In: Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, Vol. 35, 01.01.2003, p. 195-235.

Research output: Contribution to journalArticle

@article{860d9da008b24f6c9f8ce9a559c63cdc,
title = "Concentration of local energy for two-dimensional wave maps",
abstract = "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).",
keywords = "Blow-up of solution, Equivariant wave maps, H-spaces",
author = "Gueorguiev, {Vladimir Simeonov} and Angel Ivanov",
year = "2003",
month = "1",
day = "1",
language = "English",
volume = "35",
pages = "195--235",
journal = "Rendiconti dell'Istituto di Matematica dell'Universita di Trieste",
issn = "0049-4704",
publisher = "Istituto di matematica, Universita di Trieste",

}

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

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 -