{"title":"A lower bound estimate of solutions to the Cauchy problems for a hyperbolic Monge–Ampère equation","authors":"Zenggui Wang, Hui Xu, Minyuan Liu","doi":"10.1002/mma.10553","DOIUrl":null,"url":null,"abstract":"<p>This paper investigates the Cauchy problems for a hyperbolic Monge–Ampère equation which can be reduced to a quasilinear hyperbolic system via Riemannian invariants. Based on the first a priori estimate of the solutions, the second a priori estimate of the derivation of the solutions, and the third a priori estimate of the continuous mould of the first-order partial derivatives of the solutions to quasilinear hyperbolic system, a lower bound estimate of classical solutions to the Cauchy problems for a hyperbolic Monge–Ampère equation is derived.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4385-4396"},"PeriodicalIF":1.8000,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10553","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
This paper investigates the Cauchy problems for a hyperbolic Monge–Ampère equation which can be reduced to a quasilinear hyperbolic system via Riemannian invariants. Based on the first a priori estimate of the solutions, the second a priori estimate of the derivation of the solutions, and the third a priori estimate of the continuous mould of the first-order partial derivatives of the solutions to quasilinear hyperbolic system, a lower bound estimate of classical solutions to the Cauchy problems for a hyperbolic Monge–Ampère equation is derived.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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