Pub Date : 2023-10-17DOI: 10.1007/s00033-023-02120-8
Lei Zhao
Abstract The frozen-planet periodic orbit of the classical collinear Helium model with negative energy is shown to exist by a simple shooting argument. This simplifies the approach established in Cieliebak et al. (Ann Inst H Poincaré Anal Non Linéaire 40:379–455, 2022). With this argument, it also follows that the algebraic count of the number of such orbits with a given negative energy is 1, as recently established in Cieliebak et al. (Nondegeneracy and integral count of frozen-planet orbits in helium, 2022. arXiv:2209.12634 ). The same argument also leads to the existence of other collinear periodic orbits of the classical collinear Helium model.
摘要通过一个简单的射击论证，证明了负能量的经典共线氦模型的冰冻行星周期轨道的存在。这简化了Cieliebak等人建立的方法(Ann Inst H poincar Anal Non linsamaire 40:379-455, 2022)。根据这一论点，也可以得出，具有给定负能量的这种轨道的代数计数为1，正如最近在Cieliebak等人(氦中冻结行星轨道的非简并和积分计数，2022)中所建立的那样。arXiv: 2209.12634)。同样的论点也导致了经典共线氦模型的其他共线周期轨道的存在。
{"title":"Shooting for collinear periodic orbits in the Helium model","authors":"Lei Zhao","doi":"10.1007/s00033-023-02120-8","DOIUrl":"https://doi.org/10.1007/s00033-023-02120-8","url":null,"abstract":"Abstract The frozen-planet periodic orbit of the classical collinear Helium model with negative energy is shown to exist by a simple shooting argument. This simplifies the approach established in Cieliebak et al. (Ann Inst H Poincaré Anal Non Linéaire 40:379–455, 2022). With this argument, it also follows that the algebraic count of the number of such orbits with a given negative energy is 1, as recently established in Cieliebak et al. (Nondegeneracy and integral count of frozen-planet orbits in helium, 2022. arXiv:2209.12634 ). The same argument also leads to the existence of other collinear periodic orbits of the classical collinear Helium model.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994550","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}
Pub Date : 2023-10-17DOI: 10.1007/s00033-023-02122-6
Kaye Silva, Steffânio Moreno de Sousa, Carlos Alberto Santos, Minbo Yang
{"title":"Multiplicity of solutions for Brezis–Oswald-type problems with indefinite Kirchhoff operators","authors":"Kaye Silva, Steffânio Moreno de Sousa, Carlos Alberto Santos, Minbo Yang","doi":"10.1007/s00033-023-02122-6","DOIUrl":"https://doi.org/10.1007/s00033-023-02122-6","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994226","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}
Pub Date : 2023-10-17DOI: 10.1007/s00033-023-02125-3
Jing Zhang, Chunlai Mu, Xinyu Tu
{"title":"Finite-time blow-up of solution for a chemotaxis model with singular sensitivity and logistic source","authors":"Jing Zhang, Chunlai Mu, Xinyu Tu","doi":"10.1007/s00033-023-02125-3","DOIUrl":"https://doi.org/10.1007/s00033-023-02125-3","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994065","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}
Pub Date : 2023-10-16DOI: 10.1007/s00033-023-02119-1
Ning Duan, Jing Wang, Xiaopeng Zhao
{"title":"Well-posedness and large time behavior for Cahn–Hilliard–Oono equation","authors":"Ning Duan, Jing Wang, Xiaopeng Zhao","doi":"10.1007/s00033-023-02119-1","DOIUrl":"https://doi.org/10.1007/s00033-023-02119-1","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136079843","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}
Pub Date : 2023-10-16DOI: 10.1007/s00033-023-02117-3
Eudes Barboza, Yane Araújo, Gilson de Carvalho
{"title":"On nonlinear perturbations of a periodic integrodifferential Kirchhoff equation with critical exponential growth","authors":"Eudes Barboza, Yane Araújo, Gilson de Carvalho","doi":"10.1007/s00033-023-02117-3","DOIUrl":"https://doi.org/10.1007/s00033-023-02117-3","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136079468","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}
Pub Date : 2023-10-14DOI: 10.1007/s00033-023-02115-5
Meina Sun, Zhijian Wei
{"title":"The vanishing pressure limits of Riemann solutions to the isothermal two-phase flow model under the external force","authors":"Meina Sun, Zhijian Wei","doi":"10.1007/s00033-023-02115-5","DOIUrl":"https://doi.org/10.1007/s00033-023-02115-5","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135800299","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}
Pub Date : 2023-10-14DOI: 10.1007/s00033-023-02121-7
Max Heß, Guido Schneider
Abstract The derivative nonlinear Schrödinger (DNLS) equation can be derived as an amplitude equation via multiple scaling perturbation analysis for the description of the slowly varying envelope of an underlying oscillating and traveling wave packet in dispersive wave systems. It appears in the degenerated situation when the cubic coefficient of the similarly derived NLS equation vanishes. It is the purpose of this paper to prove that the DNLS approximation makes correct predictions about the dynamics of the original system under rather weak assumptions on the original dispersive wave system if we assume that the initial conditions of the DNLS equation are analytic in a strip of the complex plane. The method is presented for a Klein–Gordon model with a cubic nonlinearity.
{"title":"A robust way to justify the derivative NLS approximation","authors":"Max Heß, Guido Schneider","doi":"10.1007/s00033-023-02121-7","DOIUrl":"https://doi.org/10.1007/s00033-023-02121-7","url":null,"abstract":"Abstract The derivative nonlinear Schrödinger (DNLS) equation can be derived as an amplitude equation via multiple scaling perturbation analysis for the description of the slowly varying envelope of an underlying oscillating and traveling wave packet in dispersive wave systems. It appears in the degenerated situation when the cubic coefficient of the similarly derived NLS equation vanishes. It is the purpose of this paper to prove that the DNLS approximation makes correct predictions about the dynamics of the original system under rather weak assumptions on the original dispersive wave system if we assume that the initial conditions of the DNLS equation are analytic in a strip of the complex plane. The method is presented for a Klein–Gordon model with a cubic nonlinearity.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135800947","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}
Pub Date : 2023-10-14DOI: 10.1007/s00033-023-02113-7
Jinhuan Wang, Haomeng Chen, Mengdi Zhuang
{"title":"Global boundedness of weak solutions to a chemotaxis–haptotaxis model with p-Laplacian diffusion","authors":"Jinhuan Wang, Haomeng Chen, Mengdi Zhuang","doi":"10.1007/s00033-023-02113-7","DOIUrl":"https://doi.org/10.1007/s00033-023-02113-7","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135800514","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}
Pub Date : 2023-10-14DOI: 10.1007/s00033-023-02111-9
Timothy J. Healey
{"title":"An existence theorem for a class of wrinkling models for highly stretched elastic sheets","authors":"Timothy J. Healey","doi":"10.1007/s00033-023-02111-9","DOIUrl":"https://doi.org/10.1007/s00033-023-02111-9","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135801429","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}
Pub Date : 2023-10-14DOI: 10.1007/s00033-023-02093-8
Quanyong Zhao, Zhongping Li
{"title":"Global boundedness and large time behavior in a chemotaxis system with indirect signal consumption","authors":"Quanyong Zhao, Zhongping Li","doi":"10.1007/s00033-023-02093-8","DOIUrl":"https://doi.org/10.1007/s00033-023-02093-8","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135803344","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}
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