{"title":"次临界情况下高维非极小耦合Klein-Gordon方程的爆破动力学","authors":"M. P. Wijayanto, F. Akbar, B. Gunara","doi":"10.5614/itb.ijp.2022.33.1.5","DOIUrl":null,"url":null,"abstract":"The aim of this present work is to study the blow-up dynamics and lifespanestimate for solution to higher dimensional Klein-Gordon Equation in subcritical case, in which1 < p < psc. We construct the equation of motion from the Lagrangian of Klein-Gordon withnon-minimal coupling, where the coupling interaction of the scalar field is proportional to thescalar curvature of the spacetime. The equation of motion has the form like nonlinear dampedwave equation with mass. The novelty of this work is the time dependent of nonlinear term. Weuse test function method to proof the lifespan estimate.","PeriodicalId":13535,"journal":{"name":"Indonesian Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Blow-up Dynamics of Higher Dimensional Klein-Gordon Equation with Nonminimal Coupling in Subcritical Case\",\"authors\":\"M. P. Wijayanto, F. Akbar, B. Gunara\",\"doi\":\"10.5614/itb.ijp.2022.33.1.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this present work is to study the blow-up dynamics and lifespanestimate for solution to higher dimensional Klein-Gordon Equation in subcritical case, in which1 < p < psc. We construct the equation of motion from the Lagrangian of Klein-Gordon withnon-minimal coupling, where the coupling interaction of the scalar field is proportional to thescalar curvature of the spacetime. The equation of motion has the form like nonlinear dampedwave equation with mass. The novelty of this work is the time dependent of nonlinear term. Weuse test function method to proof the lifespan estimate.\",\"PeriodicalId\":13535,\"journal\":{\"name\":\"Indonesian Journal of Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indonesian Journal of Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5614/itb.ijp.2022.33.1.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indonesian Journal of Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5614/itb.ijp.2022.33.1.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文的目的是研究在1 < p < psc的亚临界情况下高维Klein-Gordon方程解的爆破动力学和寿命估计。我们从非极小耦合的拉格朗日方程出发，构造了标量场的耦合作用与时空的标量曲率成正比的运动方程。运动方程的形式类似于非线性带质量的阻尼波动方程。这项工作的新颖之处在于非线性项的时间依赖性。我们采用测试函数法对寿命估算进行验证。
Blow-up Dynamics of Higher Dimensional Klein-Gordon Equation with Nonminimal Coupling in Subcritical Case
The aim of this present work is to study the blow-up dynamics and lifespanestimate for solution to higher dimensional Klein-Gordon Equation in subcritical case, in which1 < p < psc. We construct the equation of motion from the Lagrangian of Klein-Gordon withnon-minimal coupling, where the coupling interaction of the scalar field is proportional to thescalar curvature of the spacetime. The equation of motion has the form like nonlinear dampedwave equation with mass. The novelty of this work is the time dependent of nonlinear term. Weuse test function method to proof the lifespan estimate.
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