{"title":"论$$(1+1)$$-维热-电模型的考希问题非扩展解的存在性","authors":"M. V. Artem’eva, M. O. Korpusov","doi":"10.1134/s0001434624050018","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider one thermal-electrical <span>\\((1+1)\\)</span>-dimensional model of heating a semiconductor in an electric field. For the corresponding Cauchy problem, we prove the existence of a classical solution nonextendable in time and obtain a global-in-time a priori estimate. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Existence of a Nonextendable Solution of the Cauchy problem for a $$(1+1)$$ -Dimensional Thermal-Electrical Model\",\"authors\":\"M. V. Artem’eva, M. O. Korpusov\",\"doi\":\"10.1134/s0001434624050018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> We consider one thermal-electrical <span>\\\\((1+1)\\\\)</span>-dimensional model of heating a semiconductor in an electric field. For the corresponding Cauchy problem, we prove the existence of a classical solution nonextendable in time and obtain a global-in-time a priori estimate. </p>\",\"PeriodicalId\":18294,\"journal\":{\"name\":\"Mathematical Notes\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Notes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0001434624050018\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0001434624050018","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Existence of a Nonextendable Solution of the Cauchy problem for a $$(1+1)$$ -Dimensional Thermal-Electrical Model
Abstract
We consider one thermal-electrical \((1+1)\)-dimensional model of heating a semiconductor in an electric field. For the corresponding Cauchy problem, we prove the existence of a classical solution nonextendable in time and obtain a global-in-time a priori estimate.
期刊介绍：
Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.
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