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Volume 19, Issue 4
A Note on “Small Amplitude Solutions of the Generalized IMBq Equation”

Youbin Zhu

J. Part. Diff. Eq., 19 (2006), pp. 377-383.

Published online: 2006-11

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  • Abstract
Global existence of small amplitude solution and nonlinear scattering result for the Cauchy problem of the generalized IMBq equation were considered in the paper titled “Small amplitude solutions of the generalized IMBq equation” [1]. It is a pity that the authors overlooked the bad behavior of low frequency part of S(t)Ψ which causes troubles in L^∞ and H^s estimates. In this note, we will present a new proof of global existence under same conditions as in [1] but for space dimension n ≥ 3.
  • Keywords

IMBq equation Duhamel's principle Hölder inequality Gronwall inequality Hausdorff-Young inequality

  • AMS Subject Headings

35L05 35L15.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-19-377, author = {}, title = {A Note on “Small Amplitude Solutions of the Generalized IMBq Equation”}, journal = {Journal of Partial Differential Equations}, year = {2006}, volume = {19}, number = {4}, pages = {377--383}, abstract = { Global existence of small amplitude solution and nonlinear scattering result for the Cauchy problem of the generalized IMBq equation were considered in the paper titled “Small amplitude solutions of the generalized IMBq equation” [1]. It is a pity that the authors overlooked the bad behavior of low frequency part of S(t)Ψ which causes troubles in L^∞ and H^s estimates. In this note, we will present a new proof of global existence under same conditions as in [1] but for space dimension n ≥ 3.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5340.html} }
TY - JOUR T1 - A Note on “Small Amplitude Solutions of the Generalized IMBq Equation” JO - Journal of Partial Differential Equations VL - 4 SP - 377 EP - 383 PY - 2006 DA - 2006/11 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5340.html KW - IMBq equation KW - Duhamel's principle KW - Hölder inequality KW - Gronwall inequality KW - Hausdorff-Young inequality AB - Global existence of small amplitude solution and nonlinear scattering result for the Cauchy problem of the generalized IMBq equation were considered in the paper titled “Small amplitude solutions of the generalized IMBq equation” [1]. It is a pity that the authors overlooked the bad behavior of low frequency part of S(t)Ψ which causes troubles in L^∞ and H^s estimates. In this note, we will present a new proof of global existence under same conditions as in [1] but for space dimension n ≥ 3.
Youbin Zhu . (2019). A Note on “Small Amplitude Solutions of the Generalized IMBq Equation”. Journal of Partial Differential Equations. 19 (4). 377-383. doi:
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