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On the square-root approximation finite volume scheme for nonlinear drift-diffusion equations 非线性漂移扩散方程的平方根近似有限体积格式
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-02-01 DOI: 10.5802/crmath.421
Clément Cancès, Juliette Venel
{"title":"On the square-root approximation finite volume scheme for nonlinear drift-diffusion equations","authors":"Clément Cancès, Juliette Venel","doi":"10.5802/crmath.421","DOIUrl":"https://doi.org/10.5802/crmath.421","url":null,"abstract":"We study a finite volume scheme for the approximation of the solution to convection diffusion equations with nonlinear convection and Robin boundary conditions. The scheme builds on the interpretation of such a continuous equation as the hydrodynamic limit of some simple exclusion jump process. We show that the scheme admits a unique discrete solution, that the natural bounds on the solution are preserved, and that it encodes the second principle of thermodynamics in the sense that some free energy is dissipated along time. The convergence of the scheme is then rigorously established thanks to compactness arguments. Numerical simulations are finally provided, highlighting the overall good behavior of the scheme.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135659035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
Brezzi–Douglas–Marini interpolation on anisotropic simplices and prisms 各向异性简单体和棱镜上的Brezzi-Douglas-Marini插值
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-01-12 DOI: 10.5802/crmath.424
Volker Kempf
{"title":"Brezzi–Douglas–Marini interpolation on anisotropic simplices and prisms","authors":"Volker Kempf","doi":"10.5802/crmath.424","DOIUrl":"https://doi.org/10.5802/crmath.424","url":null,"abstract":"The Brezzi–Douglas–Marini interpolation error on anisotropic elements has been analyzed in two recent publications, the first focusing on simplices with estimates in L 2 , the other considering parallelotopes with estimates in terms of L p -norms. This contribution provides generalized estimates for anisotropic simplices for the L p case, 1≤p≤∞, and shows new estimates for anisotropic prisms with triangular base.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135995595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Addendum to the paper: Compact embedded minimal surfaces in the Berger sphere 论文的附录:伯杰球中的致密嵌入最小表面
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-01-12 DOI: 10.5802/crmath.403
Heayong Shin, Young Wook Kim, Sung-Eun Koh, Hyung Yong Lee, Seong-Deog Yang
{"title":"Addendum to the paper: Compact embedded minimal surfaces in the Berger sphere","authors":"Heayong Shin, Young Wook Kim, Sung-Eun Koh, Hyung Yong Lee, Seong-Deog Yang","doi":"10.5802/crmath.403","DOIUrl":"https://doi.org/10.5802/crmath.403","url":null,"abstract":"We construct a two discrete parameter family of compact minimal surfaces embedded in the Berger sphere which may be considered as the analogue of the helicoidal Karcher-Scherk surfaces.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135997151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On uniform controllability of 1D transport equations in the vanishing viscosity limit 粘性消失极限下一维输运方程的均匀可控性
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-01-12 DOI: 10.5802/crmath.405
Camille Laurent, Matthieu Léautaud
{"title":"On uniform controllability of 1D transport equations in the vanishing viscosity limit","authors":"Camille Laurent, Matthieu Léautaud","doi":"10.5802/crmath.405","DOIUrl":"https://doi.org/10.5802/crmath.405","url":null,"abstract":"We consider a one dimensional transport equation with varying vector field and a small viscosity coefficient, controlled by one endpoint of the interval. We give upper and lower bounds on the minimal time needed to control to zero, uniformly in the vanishing viscosity limit.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135948610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 5
Further Equivalent Binomial Sums 进一步等价二项式和
IF 0.8 4区 数学
Comptes Rendus Mathematique Pub Date : 2021-05-27 DOI: 10.5802/CRMATH.184
M. Bai, W. Chu
{"title":"Further Equivalent Binomial Sums","authors":"M. Bai, W. Chu","doi":"10.5802/CRMATH.184","DOIUrl":"https://doi.org/10.5802/CRMATH.184","url":null,"abstract":"Five binomial sums are extended by a free parameter m, that are shown, through the generating function method, to have the same value. These sums generalize the ones by Ruehr (1980), who discovered them in the study of two unexpected equalities between definite integrals. 2020 Mathematics Subject Classification. 11B65, 05A10. Manuscript received 22nd December 2020, revised and accepted 2nd February 2021. In 1980, Kimura [14] proposed a monthly problem about two curious identities of definite integrals. If f is continuous on [− 1 2 , 3 2 ], then for δ= 0, 1, prove that ∫ 3 2 − 2 x f ( 3x −2x3)dx = 2∫ 1 0 x f ( 3x −2x3)dx. In his (trigonometric) proof, Ruehr [14] observed by linearity that to prove these identities, it is enough to verify them for monomials f (x) = xn . This led him to discover the following interesting identities An =Cn and Bn = Dn , where for a natural number n, the four binomial sums are defined by An = n ∑ j=0 3 j ( 3n − j 2n ) , Bn = n ∑ j=0 2 j ( 3n +1 2n + j +1 ) , Cn = 2n ∑ j=0 (−3) j ( 3n − j n ) , Dn = 2n ∑ j=0 (−4) j ( 3n +1 n + j +1 ) . ∗Corresponding author. ISSN (electronic) : 1778-3569 https://comptes-rendus.academie-sciences.fr/mathematique/ 422 Mei Bai and Wenchang Chu Allouche [1, 2] examined the related integrals and reviewed these identities in a more elegant manner. These identities were also reconfirmed by Meehan et al [16] who found, through the WZ-algorithm, that these four sequences satisfy also the common recurrence relation: X0 = 1 and Xn+1 = 27 4 Xn − 3 (3n+1 n ) 4(n +1) . By introducing a variable, Alzer and Prodinger [3] recently considered the polynomial analogues, that were also examined by Kilic–Arikan [13] through bijections. By applying the generating function approach to the binomial convolutions Ωn = n ∑ k=0 ( 3k k )( 3n −3k n −k ) the authors [4] not only confirmed the identities Ωn = An = Bn =Cn = Dn ; (1) but also found the two additional ones Ωn = En = Fn , (2)","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90924742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On the construction of the Śrī Yantra 关于Śrī Yantra的建设
IF 0.8 4区 数学
Comptes Rendus Mathematique Pub Date : 2021-05-27 DOI: 10.5802/CRMATH.163
A. Chiodo
{"title":"On the construction of the Śrī Yantra","authors":"A. Chiodo","doi":"10.5802/CRMATH.163","DOIUrl":"https://doi.org/10.5802/CRMATH.163","url":null,"abstract":"","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86845100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Linear dependence of quasi-periods over the rationals 拟周期对有理数的线性依赖
IF 0.8 4区 数学
Comptes Rendus Mathematique Pub Date : 2021-05-27 DOI: 10.5802/CRMATH.171
K. S. Kumar
{"title":"Linear dependence of quasi-periods over the rationals","authors":"K. S. Kumar","doi":"10.5802/CRMATH.171","DOIUrl":"https://doi.org/10.5802/CRMATH.171","url":null,"abstract":"In this note we shall show that a lattice Zω1 +Zω2 in C has Q-linearly dependent quasi-periods if and only if ω2/ω1 is equivalent to a zero of the Eisenstein series E2 under the action of SL2(Z) on the upper half plane of C. 2020 Mathematics Subject Classification. 11J72, 11J89. Manuscript received 23rd March 2020, revised 7th August 2020, accepted 17th December 2020.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86599515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On a surprising instability result of Perfectly Matched Layers for Maxwell’s equations in 3D media with diagonal anisotropy 具有对角线各向异性的三维介质中麦克斯韦方程组的完美匹配层的惊人不稳定性结果
IF 0.8 4区 数学
Comptes Rendus Mathematique Pub Date : 2021-04-20 DOI: 10.5802/CRMATH.165
É. Bécache, S. Fliss, M. Kachanovska, M. Kazakova
{"title":"On a surprising instability result of Perfectly Matched Layers for Maxwell’s equations in 3D media with diagonal anisotropy","authors":"É. Bécache, S. Fliss, M. Kachanovska, M. Kazakova","doi":"10.5802/CRMATH.165","DOIUrl":"https://doi.org/10.5802/CRMATH.165","url":null,"abstract":"The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electromagnetic wave propagation in a 3D unbounded anisotropic homogeneous medium modelled by a diagonal dielectric tensor is presented. Contrary to the 3D scalar wave equation or 2D Maxwell's equations some diagonal anisotropies lead to the existence of backward waves giving rise to instabilities of the PMLs. Numerical experiments confirm the presented result.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85403141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A new note on factored infinite series and trigonometric Fourier series 关于因式无穷级数和三角傅里叶级数的新注记
IF 0.8 4区 数学
Comptes Rendus Mathematique Pub Date : 2021-04-20 DOI: 10.5802/CRMATH.179
H. Bor
{"title":"A new note on factored infinite series and trigonometric Fourier series","authors":"H. Bor","doi":"10.5802/CRMATH.179","DOIUrl":"https://doi.org/10.5802/CRMATH.179","url":null,"abstract":"In this paper, we have proved two main theorems under more weaker conditions dealing with absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series. We have also obtained certain new results on the different absolute summability methods. 2020 Mathematics Subject Classification. 26D15, 40D15, 42A24, 46A45. Manuscript received 14th November 2020, accepted 13th January 2021.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86897353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 6
Quasihyperbolic mappings in length metric spaces 长度度量空间中的拟双曲映射
IF 0.8 4区 数学
Comptes Rendus Mathematique Pub Date : 2021-04-20 DOI: 10.5802/CRMATH.154
Qingshan Zhou, Yaxiang Li, Yuehui He
{"title":"Quasihyperbolic mappings in length metric spaces","authors":"Qingshan Zhou, Yaxiang Li, Yuehui He","doi":"10.5802/CRMATH.154","DOIUrl":"https://doi.org/10.5802/CRMATH.154","url":null,"abstract":"In this paper, we discuss the local properties of quasihyperbolic mappings in metric spaces, which are related to an open problem raised by Huang et al in 2016. Our result is a partial solution to this problem, which is also a generalization of the corresponding result obtained by Huang et al in 2016. 2020 Mathematics Subject Classification. 30L10, 53C23, 30L99, 30F10. Funding. The first author was supported by NNSF of China (No. 11901090), and by Department of Education of Guangdong Province, China (No. 2018KQNCX285). The second author was partly supported by NNSF of China (No. 11601529,11971124), and by Scientifific Research Fund of Hunan Provincial Education Department (No. 20B118). Manuscript received 9th June 2020, revised 4th October 2020, accepted 22nd November 2020.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76035154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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