The paper shows the summability of formal solutions of some linear q-difference-differential equations by using q-Laplace and q-Borel summation method.
利用q-拉普拉斯和q-Borel求和方法，证明了一些线性q-微分方程形式解的可和性。
{"title":"On the Summability of Formal Solutions of Some Linear q-Difference-Differential Equations","authors":"H. Tahara","doi":"10.1619/fesi.63.259","DOIUrl":"https://doi.org/10.1619/fesi.63.259","url":null,"abstract":"The paper shows the summability of formal solutions of some linear q-difference-differential equations by using q-Laplace and q-Borel summation method.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43335552","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}
The essential support of the symbol of a semiclassical pseudodifferentail operator is characterized by semiclassical wavefront sets of distributions. The proof employs a coherent state whose center in the phase space is dependent on Plank's constant.
{"title":"Remarks on Semiclassical Wavefront Set","authors":"Kentaro Kameoka","doi":"10.1619/fesi.64.189","DOIUrl":"https://doi.org/10.1619/fesi.64.189","url":null,"abstract":"The essential support of the symbol of a semiclassical pseudodifferentail operator is characterized by semiclassical wavefront sets of distributions. The proof employs a coherent state whose center in the phase space is dependent on Plank's constant.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43107773","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 study a nonlinear Klein-Gordon equation coupled with a Maxwell equation. Introducing a new constraint minimization problem, we prove the existence of ground states for an associated stationary elliptic system.
{"title":"On the Existence of Ground States for a Nonlinear Klein-Gordon-Maxwell Type System","authors":"M. Colin, Tatsuya Watanabe","doi":"10.1619/FESI.61.1","DOIUrl":"https://doi.org/10.1619/FESI.61.1","url":null,"abstract":"In this paper, we study a nonlinear Klein-Gordon equation coupled with a Maxwell equation. Introducing a new constraint minimization problem, we prove the existence of ground states for an associated stationary elliptic system.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81142737","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}
For spherically symmetric repulsive Hamiltonians we prove the Besov bound, the radiation condition bounds and the limiting absorption principle. The Sommerfeld uniqueness result also follows as a corollary of these. In particular, the Hamiltonians considered in this paper cover the case of inverted harmonic oscillator. In the proofs of our theorems, we mainly use a commutator argument invented recently by Ito and Skibsted. This argument is simple and elementary, and dose not employ energy cut-offs or the microlocal analysis.
{"title":"Limiting Absorption Principle and Radiation Condition for Repulsive Hamiltonians","authors":"K. Itakura","doi":"10.1619/fesi.64.199","DOIUrl":"https://doi.org/10.1619/fesi.64.199","url":null,"abstract":"For spherically symmetric repulsive Hamiltonians we prove the Besov bound, the radiation condition bounds and the limiting absorption principle. The Sommerfeld uniqueness result also follows as a corollary of these. In particular, the Hamiltonians considered in this paper cover the case of inverted harmonic oscillator. In the proofs of our theorems, we mainly use a commutator argument invented recently by Ito and Skibsted. This argument is simple and elementary, and dose not employ energy cut-offs or the microlocal analysis.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43353550","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}
This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical space-dependent damping term (DW:$V$). The main result of the present paper is to give a solution of the problem and to provide a sharp estimate for lifespan for such a solution when $frac{N}{N-1}
{"title":"Life-span of Blowup Solutions to Semilinear Wave Equation with Space-dependent Critical Damping","authors":"M. Ikeda, M. Sobajima","doi":"10.1619/fesi.64.137","DOIUrl":"https://doi.org/10.1619/fesi.64.137","url":null,"abstract":"This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical space-dependent damping term (DW:$V$). The main result of the present paper is to give a solution of the problem and to provide a sharp estimate for lifespan for such a solution when $frac{N}{N-1}<pleq p_S(N+V_0)$, where $p_S(N)$ is the Strauss exponent for (DW:$0$). The main idea of the proof is due to the technique of test functions for (DW:$0$) originated by Zhou--Han (2014, MR3169791). Moreover, we find a new threshold value $V_0=frac{(N-1)^2}{N+1}$ for the coefficient of critical and singular damping $|x|^{-1}$.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44915881","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 Cauchy problem for wave equations with unbounded damping coefficients in the whole space. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence result of a weak solution. In this case we never impose strong assumptions such as compactness of the support of the initial data. This means that we never rely on the finite propagation speed property of the solution, and we try to deal with an essential unbounded coefficient case.
{"title":"Uniform Energy Decay for Wave Equations with Unbounded Damping Coefficients","authors":"R. Ikehata, H. Takeda","doi":"10.1619/fesi.63.133","DOIUrl":"https://doi.org/10.1619/fesi.63.133","url":null,"abstract":"We consider the Cauchy problem for wave equations with unbounded damping coefficients in the whole space. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence result of a weak solution. In this case we never impose strong assumptions such as compactness of the support of the initial data. This means that we never rely on the finite propagation speed property of the solution, and we try to deal with an essential unbounded coefficient case.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46229018","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}
The aim of this paper is to prove the existence of ${mathcal R}$-bounded solution operator families for a resolvent problem on the upper half-space arising from a compressible fluid model of Korteweg type with free boundary condition. Such a compressible fluid model was derived by Dunn and Serrin (1985) and studied by Kotschote (2008) as a boundary value problem with non-slip boundary condition.
{"title":"Compressible Fluid Model of Korteweg Type with Free Boundary Condition: Model Problem","authors":"Hirokazu Saito","doi":"10.1619/fesi.62.337","DOIUrl":"https://doi.org/10.1619/fesi.62.337","url":null,"abstract":"The aim of this paper is to prove the existence of ${mathcal R}$-bounded solution operator families for a resolvent problem on the upper half-space arising from a compressible fluid model of Korteweg type with free boundary condition. Such a compressible fluid model was derived by Dunn and Serrin (1985) and studied by Kotschote (2008) as a boundary value problem with non-slip boundary condition.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49358441","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 propose a systematic study of transformations of $A$-hypergeometric functions. Our approach is to apply changes of variables corresponding to automorphisms of toric rings, to Euler-type integral representations of $A$-hypergeometric functions. We show that all linear $A$-hypergeometric transformations arise from symmetries of the corresponding polytope. As an application of the techniques developed here, we show that the Appell function $F_4$ does not admit a certain kind of Euler-type integral representation.
{"title":"On Transformations of A-Hypergeometric Functions","authors":"J. Forsgaard, L. Matusevich, Aleksandra Sobieska","doi":"10.1619/fesi.62.319","DOIUrl":"https://doi.org/10.1619/fesi.62.319","url":null,"abstract":"We propose a systematic study of transformations of $A$-hypergeometric functions. Our approach is to apply changes of variables corresponding to automorphisms of toric rings, to Euler-type integral representations of $A$-hypergeometric functions. We show that all linear $A$-hypergeometric transformations arise from symmetries of the corresponding polytope. As an application of the techniques developed here, we show that the Appell function $F_4$ does not admit a certain kind of Euler-type integral representation.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1619/fesi.62.319","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49641775","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 study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is subcritical, we show the blow-up rates and the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE argument, and lower estimates are given by a method of scaling variables.
{"title":"Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity","authors":"K. Fujiwara, M. Ikeda, Yuta Wakasugi","doi":"10.1619/fesi.62.157","DOIUrl":"https://doi.org/10.1619/fesi.62.157","url":null,"abstract":"We study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is subcritical, we show the blow-up rates and the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE argument, and lower estimates are given by a method of scaling variables.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2016-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1619/fesi.62.157","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67431464","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}
As a sequel to Kawakami-Nakamura-Sakai (arXiv:1209.3836), this series of papers constructs the complete degeneration scheme of four-dimensional Painlev'e-type equations which includes the Painlev'e-type equations associated with linear systems of ramified type. In the present paper, we consider the degeneration of Painlev'e-type equations which we call the matrix Painlev'e systems.
{"title":"Four-Dimensional Painlevé-Type Equations Associated with Ramified Linear Equations I: Matrix Painlevé Systems","authors":"H. Kawakami","doi":"10.1619/fesi.63.97","DOIUrl":"https://doi.org/10.1619/fesi.63.97","url":null,"abstract":"As a sequel to Kawakami-Nakamura-Sakai (arXiv:1209.3836), this series of papers constructs the complete degeneration scheme of four-dimensional Painlev'e-type equations which includes the Painlev'e-type equations associated with linear systems of ramified type. In the present paper, we consider the degeneration of Painlev'e-type equations which we call the matrix Painlev'e systems.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2016-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67432181","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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