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Motion by Crystalline-Like Mean Curvature: A Survey 晶体样平均曲率运动:综述
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2021-12-10 DOI: 10.1142/s1664360722300043
Y. Giga, N. Požár
{"title":"Motion by Crystalline-Like Mean Curvature: A Survey","authors":"Y. Giga, N. Požár","doi":"10.1142/s1664360722300043","DOIUrl":"https://doi.org/10.1142/s1664360722300043","url":null,"abstract":"We consider a class of anisotropic curvature flows called a crystalline curvature flow. We present a survey on this class of flows with special emphasis on the well-posedness of its initial value problem.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78662966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Existence, uniqueness, variation-of-constant formula and controllability for linear dynamic equations with Perron Δ-integrals 含Perron的线性动力方程的存在唯一性、常变公式和可控性Δ-integrals
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2021-11-30 DOI: 10.1142/s1664360721500119
F. A. da Silva, M. Federson, E. Toon
{"title":"Existence, uniqueness, variation-of-constant formula and controllability for linear dynamic equations with Perron Δ-integrals","authors":"F. A. da Silva, M. Federson, E. Toon","doi":"10.1142/s1664360721500119","DOIUrl":"https://doi.org/10.1142/s1664360721500119","url":null,"abstract":"In this paper, we investigate the existence and uniqueness of a solution for a linear Volterra-Stieltjes integral equation of the second kind, as well as for a homogeneous and a nonhomogeneous linear dynamic equations on time scales, whose integral forms contain Perron [Formula: see text]-integrals defined in Banach spaces. We also provide a variation-of-constant formula for a nonhomogeneous linear dynamic equations on time scales and we establish results on controllability for linear dynamic equations. Since we work in the framework of Perron [Formula: see text]-integrals, we can handle functions not only having many discontinuities, but also being highly oscillating. Our results require weaker conditions than those in the literature. We include some examples to illustrate our main results.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75146635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 general blow-up result for a degenerate hyperbolic inequality in an exterior domain 外域上退化双曲不等式的一般爆破结果
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2021-11-06 DOI: 10.1142/s1664360721500120
M. Jleli, M. Kirane, B. Samet
{"title":"A general blow-up result for a degenerate hyperbolic inequality in an exterior domain","authors":"M. Jleli, M. Kirane, B. Samet","doi":"10.1142/s1664360721500120","DOIUrl":"https://doi.org/10.1142/s1664360721500120","url":null,"abstract":"In this paper, we consider a degenerate hyperbolic inequality in an exterior domain under three types of boundary conditions: Dirichlet-type, Neumann-type, and Robin-type boundary conditions. Using a unified approach, we show that all the considered problems have the same Fujita critical exponent. Moreover, we answer some open questions from the literature regarding the critical case.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79320555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 survey of functional and Lp-dissipativity theory 泛函与lp耗散理论综述
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2021-11-03 DOI: 10.1142/s1664360722300031
A. Cialdea, V. Maz'ya
{"title":"A survey of functional and Lp-dissipativity theory","authors":"A. Cialdea, V. Maz'ya","doi":"10.1142/s1664360722300031","DOIUrl":"https://doi.org/10.1142/s1664360722300031","url":null,"abstract":"Various notions of dissipativity for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case [Formula: see text]-dissipativity. Most of the results are due to the authors.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91389631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Properties of the free boundary near the fixed boundary of the double obstacle problems 双障碍问题固定边界附近自由边界的性质
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2021-10-20 DOI: 10.1142/s1664360721500090
Jinwan Park
{"title":"Properties of the free boundary near the fixed boundary of the double obstacle problems","authors":"Jinwan Park","doi":"10.1142/s1664360721500090","DOIUrl":"https://doi.org/10.1142/s1664360721500090","url":null,"abstract":"In this paper, we study the tangential touch and [Formula: see text] regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obstacle problem. Then, in the classification of global solutions of the double problem, it is enough to consider only two cases for the upper obstacle, [Formula: see text] The second one is a new type of upper obstacle, which does not exist in the study of local regularity of the free boundary of the double problem. Thus, in this paper, a new type of difficulties that come from the second type upper obstacle is mainly studied.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87764495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
A Note on the Boundedness of Solutions for Fractional Relativistic Schrodinger Equations 分数阶相对论薛定谔方程解的有界性注记
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2021-10-12 DOI: 10.1142/s1664360721500107
V. Ambrosio
{"title":"A Note on the Boundedness of Solutions for Fractional Relativistic Schrodinger Equations","authors":"V. Ambrosio","doi":"10.1142/s1664360721500107","DOIUrl":"https://doi.org/10.1142/s1664360721500107","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79162039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 fourth-order Leray–Lions problem with indefinite weight and nonstandard growth conditions 不确定权值和非标准生长条件下的四阶Leray-Lions问题
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2021-10-05 DOI: 10.1142/S1664360721500089
K. Kefi, N. Irzi, M. M. Al-Shomrani, Dušan D. Repovš
{"title":"On the fourth-order Leray–Lions problem with indefinite weight and nonstandard growth conditions","authors":"K. Kefi, N. Irzi, M. M. Al-Shomrani, Dušan D. Repovš","doi":"10.1142/S1664360721500089","DOIUrl":"https://doi.org/10.1142/S1664360721500089","url":null,"abstract":"We prove the existence of at least three weak solutions for the fourth-order problem with indefinite weight involving the Leray–Lions operator with nonstandard growth conditions. The proof of our main result uses variational methods and the critical theorem of Bonanno and Marano [Appl. Anal. 89 (2010) 1–10].","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83217918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Multidimensional transonic shock waves and free boundary problems 多维跨音速激波与自由边界问题
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2021-09-21 DOI: 10.1142/S166436072230002X
Gui-Qiang G. Chen, M. Feldman
{"title":"Multidimensional transonic shock waves and free boundary problems","authors":"Gui-Qiang G. Chen, M. Feldman","doi":"10.1142/S166436072230002X","DOIUrl":"https://doi.org/10.1142/S166436072230002X","url":null,"abstract":"We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments in the analysis of multidimensional transonic shock waves and corresponding free boundary problems for the compressible Euler equations and related nonlinear partial differential equations (PDEs) of mixed type. The nonlinear PDEs under our analysis include the steady Euler equations for potential flow, the steady full Euler equations, the unsteady Euler equations for potential flow, and related nonlinear PDEs of mixed elliptic–hyperbolic type. The transonic shock problems include the problem of steady transonic flow past solid wedges, the von Neumann problem for shock reflection–diffraction, and the Prandtl–Meyer problem for unsteady supersonic flow onto solid wedges. We first show how these longstanding multidimensional transonic shock problems can be formulated as free boundary problems for the compressible Euler equations and related nonlinear PDEs of mixed type. Then we present an effective nonlinear method and related ideas and techniques to solve these free boundary problems. The method, ideas, and techniques should be useful to analyze other longstanding and newly emerging free boundary problems for nonlinear PDEs.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82691101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents 带负指数的非线性三调和及双调和方程正解的性质
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2021-08-02 DOI: 10.1142/s1664360722500072
Wei Dai, J. Fu
{"title":"On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents","authors":"Wei Dai, J. Fu","doi":"10.1142/s1664360722500072","DOIUrl":"https://doi.org/10.1142/s1664360722500072","url":null,"abstract":"In this paper, we investigate various properties (e.g., nonexistence, asymptotic behavior, uniqueness and integral representation formula) of positive solutions to nonlinear triharmonic equations in R (n ≥ 2) and bi-harmonic equations in R with negative exponents. Such kind of equations arise from conformal geometry.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90468439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Asymptotic zero distribution for a class of extremal polynomials 一类极多项式的渐近零分布
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2021-04-01 DOI: 10.1142/S166436071950019X
A. D. Gonzalez, G. Lagomasino, H. P. Cabrera
{"title":"Asymptotic zero distribution for a class of extremal polynomials","authors":"A. D. Gonzalez, G. Lagomasino, H. P. Cabrera","doi":"10.1142/S166436071950019X","DOIUrl":"https://doi.org/10.1142/S166436071950019X","url":null,"abstract":"We consider extremal polynomials with respect to a Sobolev-type [Formula: see text]-norm, with [Formula: see text] and measures supported on compact subsets of the real line. For a wide class of such extremal polynomials with respect to mutually singular measures (i.e. supported on disjoint subsets of the real line), it is proved that their critical points are simple and contained in the interior of the convex hull of the support of the measures involved and the asymptotic critical point distribution is studied. We also find the [Formula: see text]th root asymptotic behavior of the corresponding sequence of Sobolev extremal polynomials and their derivatives.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90070934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
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