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Volume 6, Issue 1
Life-span of Classical Solutions to Nonlinear Wave Equations in Two-space-dimensions II

Li Tatsien, Zhou Yi

J. Part. Diff. Eq.,6(1993),pp.17-38

Published online: 1993-06

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  • Abstract
In two-space-dimensional case we get the sharp lower bound of the life-span of classical solutions to the Cauchy problem with small initial data for fully nonlinear wave equations of the form ◻u = F (u, Du, D_zDu) in which F(\hat{λ}) = O(|\hat{λ}|^{1+α}) with α = 2 in a neighbourhood of \hat{λ} = 0. The cases α = 1 and α ≥ 3 have been considered respectively in [1] and [2].
  • Keywords

Life-span classical solution Cauchy problem nonlinear wave equation

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@Article{JPDE-6-17, author = {Li Tatsien, Zhou Yi}, title = {Life-span of Classical Solutions to Nonlinear Wave Equations in Two-space-dimensions II}, journal = {Journal of Partial Differential Equations}, year = {1993}, volume = {6}, number = {1}, pages = {17--38}, abstract = { In two-space-dimensional case we get the sharp lower bound of the life-span of classical solutions to the Cauchy problem with small initial data for fully nonlinear wave equations of the form ◻u = F (u, Du, D_zDu) in which F(\hat{λ}) = O(|\hat{λ}|^{1+α}) with α = 2 in a neighbourhood of \hat{λ} = 0. The cases α = 1 and α ≥ 3 have been considered respectively in [1] and [2].}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5698.html} }
TY - JOUR T1 - Life-span of Classical Solutions to Nonlinear Wave Equations in Two-space-dimensions II AU - Li Tatsien, Zhou Yi JO - Journal of Partial Differential Equations VL - 1 SP - 17 EP - 38 PY - 1993 DA - 1993/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5698.html KW - Life-span KW - classical solution KW - Cauchy problem KW - nonlinear wave equation AB - In two-space-dimensional case we get the sharp lower bound of the life-span of classical solutions to the Cauchy problem with small initial data for fully nonlinear wave equations of the form ◻u = F (u, Du, D_zDu) in which F(\hat{λ}) = O(|\hat{λ}|^{1+α}) with α = 2 in a neighbourhood of \hat{λ} = 0. The cases α = 1 and α ≥ 3 have been considered respectively in [1] and [2].
Li Tatsien, Zhou Yi. (1993). Life-span of Classical Solutions to Nonlinear Wave Equations in Two-space-dimensions II. Journal of Partial Differential Equations. 6 (1). 17-38. doi:
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