与某些无边网络问题有关的半群的存在性和显公式

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-18 DOI:arxiv-2409.11903

Adam Błoch

{"title":"与某些无边网络问题有关的半群的存在性和显公式","authors":"Adam Błoch","doi":"arxiv-2409.11903","DOIUrl":null,"url":null,"abstract":"In this paper we consider an initial-boundary value problem related to some\nnetwork dynamics where the underlying graph has unbounded edges. We show that\nthere exists a C0-semigroup for this problem using a general result from the\nliterature. We also find an explicit formula for this semigroup. This is\nachieved using the method of characteristics and then showing that the Laplace\ntransform of the solution is equal to the resolvent operator of the generator.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"191 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and explicit formula for a semigroup related to some network problems with unbounded edges\",\"authors\":\"Adam Błoch\",\"doi\":\"arxiv-2409.11903\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we consider an initial-boundary value problem related to some\\nnetwork dynamics where the underlying graph has unbounded edges. We show that\\nthere exists a C0-semigroup for this problem using a general result from the\\nliterature. We also find an explicit formula for this semigroup. This is\\nachieved using the method of characteristics and then showing that the Laplace\\ntransform of the solution is equal to the resolvent operator of the generator.\",\"PeriodicalId\":501035,\"journal\":{\"name\":\"arXiv - MATH - Dynamical Systems\",\"volume\":\"191 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Dynamical Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11903\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11903","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

在本文中，我们考虑了一个与一些网络动力学相关的初始边界值问题，其中底层图具有无界边。我们利用文献中的一个一般性结果，证明了该问题存在一个 C0 半群。我们还找到了这个半群的明确公式。我们利用特征法证明了解的 Laplacetransform 等于生成器的 resolvent 算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Existence and explicit formula for a semigroup related to some network problems with unbounded edges

In this paper we consider an initial-boundary value problem related to some network dynamics where the underlying graph has unbounded edges. We show that there exists a C0-semigroup for this problem using a general result from the literature. We also find an explicit formula for this semigroup. This is achieved using the method of characteristics and then showing that the Laplace transform of the solution is equal to the resolvent operator of the generator.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Dynamical Systems

自引率

0.00%

发文量