{"title":"四阶偏微分方程的非局部积分第一类条件问题","authors":"L. S. Pulkina","doi":"10.18287/2541-7525-2024-30-2-30-44","DOIUrl":null,"url":null,"abstract":"In this article, we consider a nonlocal problem with integral conditions for one-dimensional 4th order partial differential equation. A distinguishing feature of this problem is the presence of integral conditions of the 1st kind. Moreover, the kernels of these conditions depend on both spatial and time variables. We suggest a new approach which enables to overcome the difficulties arising from the form of nonlocal conditions and derive a priori estimates. Obtained estimates play a significant role when we prove the existence and uniqueness of the solution to the problem.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"9 9","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A problem with nonlocal integral 1st kind conditions for 4th order partial differential equation\",\"authors\":\"L. S. Pulkina\",\"doi\":\"10.18287/2541-7525-2024-30-2-30-44\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we consider a nonlocal problem with integral conditions for one-dimensional 4th order partial differential equation. A distinguishing feature of this problem is the presence of integral conditions of the 1st kind. Moreover, the kernels of these conditions depend on both spatial and time variables. We suggest a new approach which enables to overcome the difficulties arising from the form of nonlocal conditions and derive a priori estimates. Obtained estimates play a significant role when we prove the existence and uniqueness of the solution to the problem.\",\"PeriodicalId\":427884,\"journal\":{\"name\":\"Vestnik of Samara University. Natural Science Series\",\"volume\":\"9 9\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vestnik of Samara University. Natural Science Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18287/2541-7525-2024-30-2-30-44\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik of Samara University. Natural Science Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18287/2541-7525-2024-30-2-30-44","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A problem with nonlocal integral 1st kind conditions for 4th order partial differential equation
In this article, we consider a nonlocal problem with integral conditions for one-dimensional 4th order partial differential equation. A distinguishing feature of this problem is the presence of integral conditions of the 1st kind. Moreover, the kernels of these conditions depend on both spatial and time variables. We suggest a new approach which enables to overcome the difficulties arising from the form of nonlocal conditions and derive a priori estimates. Obtained estimates play a significant role when we prove the existence and uniqueness of the solution to the problem.
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