{"title":"关于薛定谔方程解的爆炸时间估计","authors":"Gintaras Puriuškis","doi":"10.15388/lmr.2005.24559","DOIUrl":null,"url":null,"abstract":"There is considered the Schrödinger equation ∂u/∂t= i Δu+ i|u|p , u, t > 0, with initial condition u(0, x)= u0(x), x ∈ Rn, n = 1. We prove the existence of the u0(x) such, that the blow up time estimation increases if p increases in the intervale 4 < p < p0.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"58 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Apie Šrėdingerio lygties sprendinio sprogimo laiko įvertį\",\"authors\":\"Gintaras Puriuškis\",\"doi\":\"10.15388/lmr.2005.24559\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"There is considered the Schrödinger equation ∂u/∂t= i Δu+ i|u|p , u, t > 0, with initial condition u(0, x)= u0(x), x ∈ Rn, n = 1. We prove the existence of the u0(x) such, that the blow up time estimation increases if p increases in the intervale 4 < p < p0.\",\"PeriodicalId\":33611,\"journal\":{\"name\":\"Lietuvos Matematikos Rinkinys\",\"volume\":\"58 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lietuvos Matematikos Rinkinys\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15388/lmr.2005.24559\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lietuvos Matematikos Rinkinys","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15388/lmr.2005.24559","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
薛定谔方程 ∂u/∂t= i Δu+ i|u|p , u, t > 0，初始条件为 u(0, x)= u0(x), x∈ Rn, n = 1。我们证明了 u0(x) 的存在性，即如果 p 在 4 < p < p0 的区间内增加，炸毁时间估计值会增加。
Apie Šrėdingerio lygties sprendinio sprogimo laiko įvertį
There is considered the Schrödinger equation ∂u/∂t= i Δu+ i|u|p , u, t > 0, with initial condition u(0, x)= u0(x), x ∈ Rn, n = 1. We prove the existence of the u0(x) such, that the blow up time estimation increases if p increases in the intervale 4 < p < p0.
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