{"title":"具有线性恢复力和变系数非线性的双色散方程全局解的不存在性","authors":"Natalia Kolkovska, Milena Dimova, Nikolay Kutev","doi":"10.7546/crabs.2023.10.02","DOIUrl":null,"url":null,"abstract":"We investigate Cauchy problem to double dispersion equations with polynomial type nonlinearities with variable coefficients. Necessary and sufficient conditions for nonexistence of global weak solutions and nonblowing up ones are found for subcritical initial energy. For supercritical energy a sufficient condition for finite time blow up of the weak solutions, independent of the scalar product of the initial data, is developed.","PeriodicalId":50652,"journal":{"name":"Comptes Rendus De L Academie Bulgare Des Sciences","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonexistence of Global Solutions to Double Dispersion Equations with Linear Restoring Force and Nonlinearities with Variable Coefficients\",\"authors\":\"Natalia Kolkovska, Milena Dimova, Nikolay Kutev\",\"doi\":\"10.7546/crabs.2023.10.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate Cauchy problem to double dispersion equations with polynomial type nonlinearities with variable coefficients. Necessary and sufficient conditions for nonexistence of global weak solutions and nonblowing up ones are found for subcritical initial energy. For supercritical energy a sufficient condition for finite time blow up of the weak solutions, independent of the scalar product of the initial data, is developed.\",\"PeriodicalId\":50652,\"journal\":{\"name\":\"Comptes Rendus De L Academie Bulgare Des Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus De L Academie Bulgare Des Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7546/crabs.2023.10.02\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus De L Academie Bulgare Des Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/crabs.2023.10.02","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Nonexistence of Global Solutions to Double Dispersion Equations with Linear Restoring Force and Nonlinearities with Variable Coefficients
We investigate Cauchy problem to double dispersion equations with polynomial type nonlinearities with variable coefficients. Necessary and sufficient conditions for nonexistence of global weak solutions and nonblowing up ones are found for subcritical initial energy. For supercritical energy a sufficient condition for finite time blow up of the weak solutions, independent of the scalar product of the initial data, is developed.
期刊介绍：
Founded in 1948 by academician Georgy Nadjakov, "Comptes rendus de l’Académie bulgare des Sciences" is also known as "Доклади на БАН","Доклады Болгарской академии наук" and "Proceeding of the Bulgarian Academy of Sciences".
If applicable, the name of the journal should be abbreviated as follows: C. R. Acad. Bulg. Sci. (according to ISO)
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