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PureMathematicsnØêÆ,2023,13(3),644-648
PublishedOnlineMarch2023inHans.https://www.hanspub.org/journal/pm
https://doi.org/10.12677/pm.2023.133069
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ANoteonOne-DimensionFully
NonlinearWaveEquations
XinxinXue,DongbingZha
DepartmentofMathematics,CollegeofScience,DonghuaUniversity,Shanghai
Received:Feb.22
nd
,2023;accepted:Mar.23
rd
,2023;published:Mar.30
th
,2023
Abstract
Inthispaper,westudytheCauchyproblemofone-dimensionfullynonlinearwave
equationswithnullcondition,bytransformingtheone-dimensionfullynonlinearwave
equationtoasystemofone-dimensionquasilinearwaveequations,andusingtheresult
©ÙÚ^:Å!!,ÁW.˜‘š‚5ÅÄ•§˜‡5P[J].nØêÆ,2023,13(3):644-648.
DOI:10.12677/pm.2023.133069
Å!!§ÁW
inthequasilinearcase,weshowtheglobalexistenceofclassicalsolutionwithsmall
initialdata.
Keywords
One-DimensionFullyNonlinearWaveEquations,CauchyProblem,NullCondition,
SmallInitialData,GlobalExistence
Copyright
c
2023byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution InternationalLicense(CCBY 4.0).
http://creativecommons.org/licenses/by/4.0/
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ë•©z
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Å!!§ÁW
[6]Nakamura, M. (2014) Remarks on a Weighted Energy Estimate and Its Applicationto Nonlin-
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DOI:10.12677/pm.2023.133069648nØêÆ

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