可压缩流体流过矩形多孔介质的非均质演化坝问题解的唯一性

IF 0.5 4区数学 Q3 MATHEMATICS

Glasnik Matematicki Pub Date : 2018-11-20 DOI:10.3336/gm.55.1.08

E. Zaouche

{"title":"可压缩流体流过矩形多孔介质的非均质演化坝问题解的唯一性","authors":"E. Zaouche","doi":"10.3336/gm.55.1.08","DOIUrl":null,"url":null,"abstract":"This paper is concerned with an uniqueness of solution of the weak formulation of an evolution dam problem related to a compressible fluid flow through a two-dimensional, rectangular and heterogeneous porous medium. Note that our problem associated with the equation a(x_1)(u_{x_2}+\\chi)_{x_2}-(u+\\chi)_t=0. Our technique is based on the idea that we transform the weak form of this equation into a similar situation to the proof of the uniqueness in the incompressible case (see [12]). It is also difficult to adapt the proof obtained in [12] by using some properties of the solutions as in [12, Sect. 2].","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"76 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2018-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Uniqueness of solution of a heterogeneous evolution dam problem associated with a compressible fluid flow through a rectangular porous medium\",\"authors\":\"E. Zaouche\",\"doi\":\"10.3336/gm.55.1.08\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is concerned with an uniqueness of solution of the weak formulation of an evolution dam problem related to a compressible fluid flow through a two-dimensional, rectangular and heterogeneous porous medium. Note that our problem associated with the equation a(x_1)(u_{x_2}+\\\\chi)_{x_2}-(u+\\\\chi)_t=0. Our technique is based on the idea that we transform the weak form of this equation into a similar situation to the proof of the uniqueness in the incompressible case (see [12]). It is also difficult to adapt the proof obtained in [12] by using some properties of the solutions as in [12, Sect. 2].\",\"PeriodicalId\":55601,\"journal\":{\"name\":\"Glasnik Matematicki\",\"volume\":\"76 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2018-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Glasnik Matematicki\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3336/gm.55.1.08\",\"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":"Glasnik Matematicki","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3336/gm.55.1.08","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

本文讨论了可压缩流体流过二维矩形非均质多孔介质的演化坝问题弱公式解的唯一性。注意我们的问题与方程a(x_1)(u_{x_2}+\chi)_{x_2}-(u+\chi)_t=0有关。我们的技术是基于这样一种思想，即我们将这个方程的弱形式转化为类似于不可压缩情况下唯一性证明的情况(参见[12])。用[12，第2节]中解的一些性质来改写[12]中得到的证明也是困难的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Uniqueness of solution of a heterogeneous evolution dam problem associated with a compressible fluid flow through a rectangular porous medium

This paper is concerned with an uniqueness of solution of the weak formulation of an evolution dam problem related to a compressible fluid flow through a two-dimensional, rectangular and heterogeneous porous medium. Note that our problem associated with the equation a(x_1)(u_{x_2}+\chi)_{x_2}-(u+\chi)_t=0. Our technique is based on the idea that we transform the weak form of this equation into a similar situation to the proof of the uniqueness in the incompressible case (see [12]). It is also difficult to adapt the proof obtained in [12] by using some properties of the solutions as in [12, Sect. 2].

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

Glasnik Matematicki MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Glasnik Matematicki publishes original research papers from all fields of pure and applied mathematics. The journal is published semiannually, in June and in December.