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Volume 12, Issue 1
Scattering for Semilinear Wave Equation with Small Data in High Space Dimensions

Han Yang

J. Part. Diff. Eq., 12 (1999), pp. 26-40.

Published online: 1999-12

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  • Abstract
In this paper we study the scattering theory for the semilincar wave equation u_{tt} - Δu = F(u(t, x), Du(t, x)) in R^n (n ≥ 4) with smooth and small data. We show that the scattering operator exists for the nonlinear term F = F(λ) = O(|λ|^{1, α}), where α is an integer and satisfies α ≥ 2, n = 4; α ≥ I, n ≥ 5.
  • Keywords

Semilinear wave equation scattering asymptotic behavior

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@Article{JPDE-12-26, author = {}, title = {Scattering for Semilinear Wave Equation with Small Data in High Space Dimensions}, journal = {Journal of Partial Differential Equations}, year = {1999}, volume = {12}, number = {1}, pages = {26--40}, abstract = { In this paper we study the scattering theory for the semilincar wave equation u_{tt} - Δu = F(u(t, x), Du(t, x)) in R^n (n ≥ 4) with smooth and small data. We show that the scattering operator exists for the nonlinear term F = F(λ) = O(|λ|^{1, α}), where α is an integer and satisfies α ≥ 2, n = 4; α ≥ I, n ≥ 5.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5522.html} }
TY - JOUR T1 - Scattering for Semilinear Wave Equation with Small Data in High Space Dimensions JO - Journal of Partial Differential Equations VL - 1 SP - 26 EP - 40 PY - 1999 DA - 1999/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5522.html KW - Semilinear wave equation KW - scattering KW - asymptotic behavior AB - In this paper we study the scattering theory for the semilincar wave equation u_{tt} - Δu = F(u(t, x), Du(t, x)) in R^n (n ≥ 4) with smooth and small data. We show that the scattering operator exists for the nonlinear term F = F(λ) = O(|λ|^{1, α}), where α is an integer and satisfies α ≥ 2, n = 4; α ≥ I, n ≥ 5.
Han Yang . (2019). Scattering for Semilinear Wave Equation with Small Data in High Space Dimensions. Journal of Partial Differential Equations. 12 (1). 26-40. doi:
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