{"title":"具有奇异敏感性的脱发症高维趋化系统的有界性","authors":"","doi":"10.1016/j.aml.2024.109231","DOIUrl":null,"url":null,"abstract":"<div><p>This paper deals with a fully parabolic chemotaxis system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><msub><mrow><mi>χ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mfrac><mrow><mi>u</mi></mrow><mrow><mi>w</mi></mrow></mfrac><mo>∇</mo><mi>w</mi><mo>)</mo></mrow><mo>+</mo><mi>w</mi><mo>−</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><msub><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mi>w</mi></mrow></mfrac><mo>∇</mo><mi>w</mi><mo>)</mo></mrow><mo>+</mo><mi>w</mi><mo>+</mo><mi>r</mi><mi>u</mi><mi>v</mi><mo>−</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>+</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>−</mo><mi>w</mi><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>in a bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mrow><mo>(</mo><mi>n</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> with smooth boundary, where <span><math><mrow><mi>r</mi><mo>></mo><mn>0</mn><mo>,</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>></mo><mn>0</mn><mo>,</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>></mo><mn>0</mn><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow><mo>.</mo></mrow></math></span> Under the condition <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≥</mo><mn>2</mn><mi>r</mi><mo>,</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≥</mo><mn>2</mn><mi>r</mi><mo>,</mo><mo>max</mo><mrow><mo>{</mo><msub><mrow><mi>χ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>}</mo></mrow><mo><</mo><msqrt><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt><mo>,</mo></mrow></math></span> it is shown that the corresponding system possesses a globally bounded classical solution, which extends the previous boundedness result from <span><math><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></math></span> to <span><math><mrow><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></math></span>.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Boundedness in the higher-dimensional chemotaxis system for Alopecia Areata with singular sensitivity\",\"authors\":\"\",\"doi\":\"10.1016/j.aml.2024.109231\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper deals with a fully parabolic chemotaxis system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><msub><mrow><mi>χ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mfrac><mrow><mi>u</mi></mrow><mrow><mi>w</mi></mrow></mfrac><mo>∇</mo><mi>w</mi><mo>)</mo></mrow><mo>+</mo><mi>w</mi><mo>−</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><msub><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mi>w</mi></mrow></mfrac><mo>∇</mo><mi>w</mi><mo>)</mo></mrow><mo>+</mo><mi>w</mi><mo>+</mo><mi>r</mi><mi>u</mi><mi>v</mi><mo>−</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>+</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>−</mo><mi>w</mi><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>in a bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mrow><mo>(</mo><mi>n</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> with smooth boundary, where <span><math><mrow><mi>r</mi><mo>></mo><mn>0</mn><mo>,</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>></mo><mn>0</mn><mo>,</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>></mo><mn>0</mn><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow><mo>.</mo></mrow></math></span> Under the condition <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≥</mo><mn>2</mn><mi>r</mi><mo>,</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≥</mo><mn>2</mn><mi>r</mi><mo>,</mo><mo>max</mo><mrow><mo>{</mo><msub><mrow><mi>χ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>}</mo></mrow><mo><</mo><msqrt><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt><mo>,</mo></mrow></math></span> it is shown that the corresponding system possesses a globally bounded classical solution, which extends the previous boundedness result from <span><math><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></math></span> to <span><math><mrow><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></math></span>.</p></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965924002519\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924002519","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Boundedness in the higher-dimensional chemotaxis system for Alopecia Areata with singular sensitivity
This paper deals with a fully parabolic chemotaxis system in a bounded domain with smooth boundary, where Under the condition it is shown that the corresponding system possesses a globally bounded classical solution, which extends the previous boundedness result from to .
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.