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Dynamics of Partial Differential Equations最新文献

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On blow-up solutions to the nonlinear Schrödinger equation in the exterior of a convex obstacle 凸障碍物外部非线性Schrödinger方程的爆破解
IF 1.3 3区 数学
Dynamics of Partial Differential Equations Pub Date : 2020-12-24 DOI: 10.4310/dpde.2022.v19.n1.a1
O. Landoulsi
{"title":"On blow-up solutions to the nonlinear Schrödinger equation in the exterior of a convex obstacle","authors":"O. Landoulsi","doi":"10.4310/dpde.2022.v19.n1.a1","DOIUrl":"https://doi.org/10.4310/dpde.2022.v19.n1.a1","url":null,"abstract":"In this paper, we consider the Schrödinger equation with a mass-supercritical focusing nonlinearity, in the exterior of a smooth, compact, convex obstacle of R with Dirichlet boundary conditions. We prove that solutions with negative energy blow up in finite time. Assuming furthermore that the nonlinearity is energy-subcritical, we also prove (under additional symmetry conditions) blow-up with the same optimal ground-state criterion than in the work of Holmer and Roudenko on R. The classical proof of Glassey, based on the concavity of the variance, fails in the exterior of an obstacle because of the appearance of boundary terms with an unfavorable sign in the second derivative of the variance. The main idea of our proof is to introduce a new modified variance which is bounded from below and strictly concave for the solutions that we consider.","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44488636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Second- and Higher-Order Linear Partial Differential Equations 二阶和高阶线性偏微分方程
IF 1.3 3区 数学
Dynamics of Partial Differential Equations Pub Date : 2020-12-01 DOI: 10.1201/9781003105183-3
Nita H. Shah, Mrudul Y. Jani
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引用次数: 0
Introduction of Partial Differential Equations 偏微分方程导论
IF 1.3 3区 数学
Dynamics of Partial Differential Equations Pub Date : 2020-12-01 DOI: 10.1201/9781003105183-1
Nita H. Shah, Mrudul Y. Jani
{"title":"Introduction of Partial Differential Equations","authors":"Nita H. Shah, Mrudul Y. Jani","doi":"10.1201/9781003105183-1","DOIUrl":"https://doi.org/10.1201/9781003105183-1","url":null,"abstract":"","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":"320 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77560264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Applications of Partial Differential Equations 偏微分方程的应用
IF 1.3 3区 数学
Dynamics of Partial Differential Equations Pub Date : 2020-12-01 DOI: 10.1201/9781003105183-4
Nita H. Shah, Mrudul Y. Jani
{"title":"Applications of Partial Differential Equations","authors":"Nita H. Shah, Mrudul Y. Jani","doi":"10.1201/9781003105183-4","DOIUrl":"https://doi.org/10.1201/9781003105183-4","url":null,"abstract":"","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":"27 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83744295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Strichartz estimates for wave and Dirac equations in Aharonov–Bohm magnetic fields Aharonov-Bohm磁场中波动方程和狄拉克方程的广义Strichartz估计
IF 1.3 3区 数学
Dynamics of Partial Differential Equations Pub Date : 2020-08-01 DOI: 10.4310/dpde.2022.v19.n1.a4
F. Cacciafesta, Zhiqing Yin, Junyong Zhang
{"title":"Generalized Strichartz estimates for wave and Dirac equations in Aharonov–Bohm magnetic fields","authors":"F. Cacciafesta, Zhiqing Yin, Junyong Zhang","doi":"10.4310/dpde.2022.v19.n1.a4","DOIUrl":"https://doi.org/10.4310/dpde.2022.v19.n1.a4","url":null,"abstract":"We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well established strategy to deal with scaling critical perturbations of dispersive PDEs, we make use of Hankel transform and rely on some precise estimates on Bessel functions. As a complementary result, we prove a local smoothing estimate for the Klein-Gordon equation in the same magnetic field.","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47405270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Global well-posedness for the fifth-order Kadomtsev–Petviashvili II equation in anisotropic Gevrey spaces 各向异性Gevrey空间中五阶Kadomtsev–Petviashvili II方程的全局适定性
IF 1.3 3区 数学
Dynamics of Partial Differential Equations Pub Date : 2020-06-23 DOI: 10.4310/DPDE.2021.V18.N2.A2
A. Boukarou, Daniel Oliveira da Silva, K. Guerbati, K. Zennir
{"title":"Global well-posedness for the fifth-order Kadomtsev–Petviashvili II equation in anisotropic Gevrey spaces","authors":"A. Boukarou, Daniel Oliveira da Silva, K. Guerbati, K. Zennir","doi":"10.4310/DPDE.2021.V18.N2.A2","DOIUrl":"https://doi.org/10.4310/DPDE.2021.V18.N2.A2","url":null,"abstract":"We show that the fifth-order Kadomtsev-Petviashvili II equation is globally well-posed in an anisotropic Gevrey space, which complements earlier results on the well-posedness of this equation in anisotropic Sobolev spaces.","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45025870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
7. Method of characteristics for first-order quasilinear equations 7. 一阶拟线性方程的特征方法
IF 1.3 3区 数学
Dynamics of Partial Differential Equations Pub Date : 2020-06-08 DOI: 10.1515/9783110677256-007
{"title":"7. Method of characteristics for first-order quasilinear equations","authors":"","doi":"10.1515/9783110677256-007","DOIUrl":"https://doi.org/10.1515/9783110677256-007","url":null,"abstract":"","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":"48 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88236942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
3. First-order linear equations 3.。一阶线性方程
IF 1.3 3区 数学
Dynamics of Partial Differential Equations Pub Date : 2020-06-08 DOI: 10.1515/9783110677256-003
{"title":"3. First-order linear equations","authors":"","doi":"10.1515/9783110677256-003","DOIUrl":"https://doi.org/10.1515/9783110677256-003","url":null,"abstract":"","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":"19 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79026425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
6. First-order quasilinear equations: solution sets 6. 一阶拟线性方程:解集
IF 1.3 3区 数学
Dynamics of Partial Differential Equations Pub Date : 2020-06-08 DOI: 10.1515/9783110677256-006
{"title":"6. First-order quasilinear equations: solution sets","authors":"","doi":"10.1515/9783110677256-006","DOIUrl":"https://doi.org/10.1515/9783110677256-006","url":null,"abstract":"","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":"1943 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91189816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
4. First-order semilinear equations 4. 一阶半线性方程
IF 1.3 3区 数学
Dynamics of Partial Differential Equations Pub Date : 2020-06-08 DOI: 10.1515/9783110677256-004
{"title":"4. First-order semilinear equations","authors":"","doi":"10.1515/9783110677256-004","DOIUrl":"https://doi.org/10.1515/9783110677256-004","url":null,"abstract":"","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":"3 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78137512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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