由随机测量驱动的布尔格斯型方程

Pub Date : 2024-05-10 DOI:10.1090/tpms/1213

Vadym Radchenko

{"title":"由随机测量驱动的布尔格斯型方程","authors":"Vadym Radchenko","doi":"10.1090/tpms/1213","DOIUrl":null,"url":null,"abstract":"We study the one-dimensional equation driven by a stochastic measure \n\n \n μ\n \\mu\n \n\n. For \n\n \n μ\n \\mu\n \n\n we assume only \n\n \n σ\n \\sigma\n \n\n-additivity in probability. Our results imply the global existence and uniqueness of the solution to the heat equation and the local existence and uniqueness of the solution to the Burgers equation. The averaging principle for such equation is studied.","PeriodicalId":0,"journal":{"name":"","volume":" 0","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Burgers-type equation driven by a stochastic measure\",\"authors\":\"Vadym Radchenko\",\"doi\":\"10.1090/tpms/1213\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the one-dimensional equation driven by a stochastic measure \\n\\n \\n μ\\n \\\\mu\\n \\n\\n. For \\n\\n \\n μ\\n \\\\mu\\n \\n\\n we assume only \\n\\n \\n σ\\n \\\\sigma\\n \\n\\n-additivity in probability. Our results imply the global existence and uniqueness of the solution to the heat equation and the local existence and uniqueness of the solution to the Burgers equation. The averaging principle for such equation is studied.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":\" 0\",\"pages\":\"\"},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/tpms/1213\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tpms/1213","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

我们研究由随机度量 μ \mu 驱动的一元方程。对于 μ \mu，我们只假设概率的 σ σ -加性。我们的结果意味着热方程解的全局存在性和唯一性，以及布尔格斯方程解的局部存在性和唯一性。研究了此类方程的平均原理。

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

The Burgers-type equation driven by a stochastic measure

We study the one-dimensional equation driven by a stochastic measure μ \mu . For μ \mu we assume only σ \sigma -additivity in probability. Our results imply the global existence and uniqueness of the solution to the heat equation and the local existence and uniqueness of the solution to the Burgers equation. The averaging principle for such equation is studied.

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