抛物线双相障碍问题

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Siegfried Carl , Patrick Winkert
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The obstacle is represented by the closed convex set <span><math><mi>K</mi></math></span> with the obstacle function <span><math><mi>ψ</mi></math></span> through <span><span><span><math><mrow><mi>K</mi><mo>=</mo><mrow><mo>{</mo><mi>v</mi><mo>∈</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mspace></mspace><mo>:</mo><mspace></mspace><mi>v</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>≤</mo><mi>ψ</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mtext>for a.a.</mtext><mspace></mspace><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>∈</mo><mi>Q</mi><mo>=</mo><mi>Ω</mi><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>τ</mi><mo>)</mo></mrow><mo>}</mo></mrow></mrow></math></span></span></span>and <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> is the indicator function related to <span><math><mi>K</mi></math></span> with <span><math><mrow><mi>∂</mi><msub><mrow><mi>I</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow></math></span> denoting its subdifferential in the sense of convex analysis.</p></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S1468121824001093/pdfft?md5=8c45c9bac4bc0752dc7ba149da99cd83&pid=1-s2.0-S1468121824001093-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1468121824001093\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824001093","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

我们证明了抛物线双相障碍问题的存在性结果:在 u(⋅,0)=0 时找到 u∈K⊂X0 满足 0∈ut+Au+F(u)+∂IK(u)inX0∗ 的 u∈K⊂X0,其中,A:X0→X0∗,Au≔-div|∇u|p-2∇u+μ(x)|∇u|q-2∇uforu∈X0,是作用于 X0=Lp(0,τ;W01,H(Ω))的双相算子,W01,H(Ω)表示具有广义同质边界值的相关穆西拉克-奥利兹索博廖夫空间。障碍由封闭凸集 K 表示,障碍函数 ψ 通过 K={v∈X0:v(x,t)≤ψ(x,t)for a.a.(x,t)∈Q=Ω×(0,τ)} 表示,IK 是与 K 相关的指示函数,∂IK 表示其在凸分析意义上的次微分。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Parabolic double phase obstacle problems

We prove existence results for the parabolic double phase obstacle problem: Find uKX0 with u(,0)=0 satisfying 0ut+Au+F(u)+IK(u)inX0,where A:X0X0 given by Audiv|u|p2u+μ(x)|u|q2uforuX0,is the double phase operator acting on X0=Lp(0,τ;W01,H(Ω)) with W01,H(Ω) denoting the associated Musielak–Orlicz Sobolev space with generalized homogeneous boundary values. The obstacle is represented by the closed convex set K with the obstacle function ψ through K={vX0:v(x,t)ψ(x,t)for a.a.(x,t)Q=Ω×(0,τ)}and IK is the indicator function related to K with IK denoting its subdifferential in the sense of convex analysis.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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