{"title":"三角形各向同性反应扩散系统:在纹理合成中的应用","authors":"M. A. Oussous, N. Alaa","doi":"10.12988/IJMA.2013.35106","DOIUrl":null,"url":null,"abstract":"This work is devoted to the existence of weak solutions for m × m isotropic reaction-diffusion systems. This type of system appears in texture synthesis. The originality of this study persists in the fact that the non-linearities considered here involve the gradients of solutions with arbitrary growth and initial data are only in L 2 (Ω). For this reason, New techniques are needed to show the consistency of these models is that we present in this study showing the global existence of weak solutions. Mathematics Subject Classification: 35J20, 35J25, 35J65, 45H15","PeriodicalId":431531,"journal":{"name":"International Journal of Mathematical Analysis","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Triangular Isotropic Reaction-Diffusion Systems: Application to Texture Synthesis\",\"authors\":\"M. A. Oussous, N. Alaa\",\"doi\":\"10.12988/IJMA.2013.35106\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work is devoted to the existence of weak solutions for m × m isotropic reaction-diffusion systems. This type of system appears in texture synthesis. The originality of this study persists in the fact that the non-linearities considered here involve the gradients of solutions with arbitrary growth and initial data are only in L 2 (Ω). For this reason, New techniques are needed to show the consistency of these models is that we present in this study showing the global existence of weak solutions. Mathematics Subject Classification: 35J20, 35J25, 35J65, 45H15\",\"PeriodicalId\":431531,\"journal\":{\"name\":\"International Journal of Mathematical Analysis\",\"volume\":\"43 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/IJMA.2013.35106\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/IJMA.2013.35106","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Triangular Isotropic Reaction-Diffusion Systems: Application to Texture Synthesis
This work is devoted to the existence of weak solutions for m × m isotropic reaction-diffusion systems. This type of system appears in texture synthesis. The originality of this study persists in the fact that the non-linearities considered here involve the gradients of solutions with arbitrary growth and initial data are only in L 2 (Ω). For this reason, New techniques are needed to show the consistency of these models is that we present in this study showing the global existence of weak solutions. Mathematics Subject Classification: 35J20, 35J25, 35J65, 45H15
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