{"title":"Differential Algebraicity of the Multiple Elliptic Gamma Function for a Rational Period","authors":"Masakimi Kato","doi":"10.1619/fesi.64.225","DOIUrl":"https://doi.org/10.1619/fesi.64.225","url":null,"abstract":"","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48466215","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}
In this paper we investigate the Cauchy problem for hyperbolic operators with double characteristics in the framework of the space of C∞ functions. In the case where the coefficients of their principal parts depend only on the time variable and are real analytic, we give a sufficient condition for C∞ well-posedness, which is also a necessary one when the space dimension is less than 3 or the coefficients of the principal parts are semi-algebraic functions ( e.g., polynomials) of the time variable.
{"title":"On the Cauchy Problem for Hyperbolic Operators with Double Characteristics whose Principal Parts Have Time Dependent Coefficients","authors":"S. Wakabayashi","doi":"10.1619/fesi.63.345","DOIUrl":"https://doi.org/10.1619/fesi.63.345","url":null,"abstract":"In this paper we investigate the Cauchy problem for hyperbolic operators with double characteristics in the framework of the space of C∞ functions. In the case where the coefficients of their principal parts depend only on the time variable and are real analytic, we give a sufficient condition for C∞ well-posedness, which is also a necessary one when the space dimension is less than 3 or the coefficients of the principal parts are semi-algebraic functions ( e.g., polynomials) of the time variable.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41577987","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}
{"title":"Wellposedness and Asymptotic Behavior of the Perturbed Nonlinear Schrödinger Equation with Kerr Law Nonlinearity and Localized Damping","authors":"Zai-yun Zhang, Zhenhai Liu, Ming-bao Sun","doi":"10.1619/fesi.63.293","DOIUrl":"https://doi.org/10.1619/fesi.63.293","url":null,"abstract":"","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48290328","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}
{"title":"Equivalence of Viscosity Solutions between Obstacle and Gradient Constraint Problems","authors":"T. Kosugi","doi":"10.1619/fesi.63.323","DOIUrl":"https://doi.org/10.1619/fesi.63.323","url":null,"abstract":"","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44767079","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}
We prove low regularity a priori estimates for the derivative nonlinear Schrodinger equation in Besov spaces with positive regularity index conditional upon small $L^2$ -norm. This covers the full subcritical range. We use the power series expansion of the perturbation determinant introduced by Killip–Visan–Zhang for completely integrable PDE. This makes it possible to derive low regularity conservation laws from the perturbation determinant.
{"title":"A Priori Estimates for the Derivative Nonlinear Schrödinger Equation","authors":"Friedrich Klaus, R. Schippa","doi":"10.1619/fesi.65.329","DOIUrl":"https://doi.org/10.1619/fesi.65.329","url":null,"abstract":"We prove low regularity a priori estimates for the derivative nonlinear Schrodinger equation in Besov spaces with positive regularity index conditional upon small $L^2$ -norm. This covers the full subcritical range. We use the power series expansion of the perturbation determinant introduced by Killip–Visan–Zhang for completely integrable PDE. This makes it possible to derive low regularity conservation laws from the perturbation determinant.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49142116","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}
We consider the large time behavior of the three-dimensional Navier-Stokes flow around a rotating rigid body. Assume that the angular velocity of the body gradually increases until it reaches a small terminal one at a certain finite time and it is fixed afterwards. We then show that the fluid motion converges to a steady solution as time $trightarrowinfty$.
{"title":"Attainability of a Stationary Navier-Stokes Flow around a Rigid Body Rotating from Rest","authors":"T. Takahashi","doi":"10.1619/fesi.65.111","DOIUrl":"https://doi.org/10.1619/fesi.65.111","url":null,"abstract":"We consider the large time behavior of the three-dimensional Navier-Stokes flow around a rotating rigid body. Assume that the angular velocity of the body gradually increases until it reaches a small terminal one at a certain finite time and it is fixed afterwards. We then show that the fluid motion converges to a steady solution as time $trightarrowinfty$.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46015403","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}
In this paper using a transform defined by the translation operator we introduce the concept of spectrum of sequences that are bounded by $n^nu$, where $nu$ is a natural number. We apply this spectral theory to study the asymptotic behavior of solutions of fractional difference equations of the form $Delta^alpha x(n)=Tx(n)+y(n)$, $nin mathbb{N}$, where $0
{"title":"A Spectral Theory of Polynomially Bounded Sequences and Applications to the Asymptotic Behavior of Discrete Systems","authors":"N. Minh, H. Matsunaga, N. D. Huy, V. Luong","doi":"10.1619/fesi.65.261","DOIUrl":"https://doi.org/10.1619/fesi.65.261","url":null,"abstract":"In this paper using a transform defined by the translation operator we introduce the concept of spectrum of sequences that are bounded by $n^nu$, where $nu$ is a natural number. We apply this spectral theory to study the asymptotic behavior of solutions of fractional difference equations of the form $Delta^alpha x(n)=Tx(n)+y(n)$, $nin mathbb{N}$, where $0<alphale 1$. One of the obtained results is an extension of a famous Katznelson-Tzafriri Theorem, saying that if the $alpha$-resolvent operator $S_alpha$ satisfies $sup_{ninmathbb{N}} | S_alpha (n)| /n^nu <infty$ and the set of $z_0in mathbb{C}$ such that $(z-tilde k^alpha (z)T)^{-1}$ exists, and together with $tilde k^alpha (z)$, is holomorphic in a neighborhood of $z_0$ consists of at most $1$, where $ tilde k^alpha (z)$ is the Z-transform of $k^alpha (n):= Gamma (alpha +n)/(Gamma (alpha )Gamma (n+1))$, then begin{align*} lim_{nto infty} frac{1}{n^nu} sum_{k=0}^{nu+1} frac{(nu+1)!}{k!(nu+1-k)!} (-1)^{nu+1+k} S_alpha (n+k) =0. end{align*}","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47290015","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}
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