{"title":"一阶偏微分方程","authors":"C. E. Gutiérrez","doi":"10.1142/9789813270886_0011","DOIUrl":null,"url":null,"abstract":"1. Systems of 1st order ordinary differential equations 2 1.1. Existence of solutions 2 1.2. Uniqueness 4 1.3. Differentiability of solutions with respect to a parameter 6 2. Quasi-linear pdes 10 2.1. Step 1 10 2.2. Step 2 11 2.3. Cauchy problem 11 3. Degenerate case 12 4. Examples 14 4.1. Example 1 14 4.2. Example 2 14 4.3. Example 3 14 4.4. A maximum principle for a first order pde 15 5. Fully nonlinear case 15 5.1. Cauchy problem 17 5.2. Uniqueness 21 5.3. Solution of the eikonal equation 22 5.4. Higher dimensional case 23 6. A transversality problem 24 7. The Legendre transform 25 References 27","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"45 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"First Order PDEs\",\"authors\":\"C. E. Gutiérrez\",\"doi\":\"10.1142/9789813270886_0011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"1. Systems of 1st order ordinary differential equations 2 1.1. Existence of solutions 2 1.2. Uniqueness 4 1.3. Differentiability of solutions with respect to a parameter 6 2. Quasi-linear pdes 10 2.1. Step 1 10 2.2. Step 2 11 2.3. Cauchy problem 11 3. Degenerate case 12 4. Examples 14 4.1. Example 1 14 4.2. Example 2 14 4.3. Example 3 14 4.4. A maximum principle for a first order pde 15 5. Fully nonlinear case 15 5.1. Cauchy problem 17 5.2. Uniqueness 21 5.3. Solution of the eikonal equation 22 5.4. Higher dimensional case 23 6. A transversality problem 24 7. The Legendre transform 25 References 27\",\"PeriodicalId\":233526,\"journal\":{\"name\":\"Linear Mathematical Models in Chemical Engineering\",\"volume\":\"45 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Linear Mathematical Models in Chemical Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/9789813270886_0011\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Mathematical Models in Chemical Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789813270886_0011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
1. Systems of 1st order ordinary differential equations 2 1.1. Existence of solutions 2 1.2. Uniqueness 4 1.3. Differentiability of solutions with respect to a parameter 6 2. Quasi-linear pdes 10 2.1. Step 1 10 2.2. Step 2 11 2.3. Cauchy problem 11 3. Degenerate case 12 4. Examples 14 4.1. Example 1 14 4.2. Example 2 14 4.3. Example 3 14 4.4. A maximum principle for a first order pde 15 5. Fully nonlinear case 15 5.1. Cauchy problem 17 5.2. Uniqueness 21 5.3. Solution of the eikonal equation 22 5.4. Higher dimensional case 23 6. A transversality problem 24 7. The Legendre transform 25 References 27
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