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Well-Posedness for the Two-Dimensional Zakharov-Kuznetsov Equation 二维Zakharov-Kuznetsov方程的适定性
IF 0.3 4区 数学
Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2020-01-01 DOI: 10.1619/FESI.63.67
Minjie Shan
{"title":"Well-Posedness for the Two-Dimensional Zakharov-Kuznetsov Equation","authors":"Minjie Shan","doi":"10.1619/FESI.63.67","DOIUrl":"https://doi.org/10.1619/FESI.63.67","url":null,"abstract":"","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67432172","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
Global Existence and Decay Estimates for the Heat Equation with Exponential Nonlinearity 指数非线性热方程的整体存在性和衰减估计
IF 0.3 4区 数学
Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2019-12-12 DOI: 10.1619/fesi.64.237
M. Majdoub, S. Tayachi
{"title":"Global Existence and Decay Estimates for the Heat Equation with Exponential Nonlinearity","authors":"M. Majdoub, S. Tayachi","doi":"10.1619/fesi.64.237","DOIUrl":"https://doi.org/10.1619/fesi.64.237","url":null,"abstract":"In this paper we consider the initial value {problem $partial_{t} u- Delta u=f(u),$ $u(0)=u_0in exp,L^p(mathbb{R}^N),$} where $p>1$ and $f : mathbb{R}tomathbb{R}$ having an exponential growth at infinity with $f(0)=0.$ Under smallness condition on the initial data and for nonlinearity $f$ {such that $|f(u)|sim mbox{e}^{|u|^q}$ as $|u|to infty$,} $|f(u)|sim |u|^{m}$ as $uto 0,$ $0 1$, we show that the solution is global. Moreover, we obtain decay estimates in Lebesgue spaces for large time which depend on $m.$","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41387671","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
Well-posedness for the Cauchy Problem of the Modified Zakharov-Kuznetsov Equation 修正Zakharov-Kuznetsov方程Cauchy问题的适定性
IF 0.3 4区 数学
Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2019-11-29 DOI: 10.1619/fesi.65.139
S. Kinoshita
{"title":"Well-posedness for the Cauchy Problem of the Modified Zakharov-Kuznetsov Equation","authors":"S. Kinoshita","doi":"10.1619/fesi.65.139","DOIUrl":"https://doi.org/10.1619/fesi.65.139","url":null,"abstract":"This paper is concerned with the Cauchy problem of the modified Zakharov-Kuznetsov equation on $mathbb{R}^d$. If $d=2$, we prove the sharp estimate which implies local in time well-posedness in the Sobolev space $H^s(mathbb{R}^2)$ for $s geq 1/4$. If $d geq 3$, by employing $U^p$ and $V^p$ spaces, we establish the small data global well-posedness in the scaling critical Sobolev space $H^{s_c}(mathbb{R}^d)$ where $s_c = d/2-1$.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42224725","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: 11
Variants of q-Hypergeometric Equation q-超几何方程的变体
IF 0.3 4区 数学
Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2019-10-28 DOI: 10.1619/fesi.65.159
N. Hatano, Ryuya Matsunawa, Tomoki Sato, K. Takemura
{"title":"Variants of q-Hypergeometric Equation","authors":"N. Hatano, Ryuya Matsunawa, Tomoki Sato, K. Takemura","doi":"10.1619/fesi.65.159","DOIUrl":"https://doi.org/10.1619/fesi.65.159","url":null,"abstract":"We introduce two variants of $q$-hypergeometric equation. We obtain several explicit solutions of variants of $q$-hypergeometric equation. We show that a variant of $q$-hypergeometric equation can be obtained by a restriction of $q$-Appell equation of two variables.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46314776","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
Gevrey Regularity for a System Coupling the Navier-Stokes System with a Beam: the Non-Flat Case Navier-Stokes系统与梁耦合系统的Gevrey正则性:非平坦情况
IF 0.3 4区 数学
Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2019-10-16 DOI: 10.1619/fesi.65.63
Mehdi Badra, Takéo Takahashi
{"title":"Gevrey Regularity for a System Coupling the Navier-Stokes System with a Beam: the Non-Flat Case","authors":"Mehdi Badra, Takéo Takahashi","doi":"10.1619/fesi.65.63","DOIUrl":"https://doi.org/10.1619/fesi.65.63","url":null,"abstract":"We consider a bi-dimensional viscous incompressible fluid in interaction with a beam located at its boundary. We show the existence of strong solutions for this fluid-structure interaction system, extending a previous result where we supposed that the initial deformation of the beam was small. The main point of the proof consists in the study of the linearized system and in particular in proving that the corresponding semigroup is of Gevrey class.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43833748","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: 8
Global Well-Posedness of the 4-D Energy-Critical Stochastic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Condition 具有非消失边界条件的四维能量临界随机非线性Schrödinger方程的全局适定性
IF 0.3 4区 数学
Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2019-10-07 DOI: 10.1619/fesi.65.287
Kelvin Cheung, Guopeng Li
{"title":"Global Well-Posedness of the 4-D Energy-Critical Stochastic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Condition","authors":"Kelvin Cheung, Guopeng Li","doi":"10.1619/fesi.65.287","DOIUrl":"https://doi.org/10.1619/fesi.65.287","url":null,"abstract":"We consider the energy-critical stochastic cubic nonlinear Schrodinger equation on $mathbb R^4$ with additive noise, and with the non-vanishing boundary conditions at spatial infinity. By viewing this equation as a perturbation to the energy-critical cubic nonlinear Schrodinger equation on $mathbb R^4$, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43250963","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
Time Decay Estimate with Diffusion Wave Property and Smoothing Effect for Solutions to the Compressible Navier-Stokes-Korteweg System 可压缩Navier-Stokes-Korteweg系统解具有扩散波性质和平滑效应的时间衰减估计
IF 0.3 4区 数学
Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2019-05-31 DOI: 10.1619/fesi.64.163
Takayuki Kobayashi, Kazuyuki Tsuda
{"title":"Time Decay Estimate with Diffusion Wave Property and Smoothing Effect for Solutions to the Compressible Navier-Stokes-Korteweg System","authors":"Takayuki Kobayashi, Kazuyuki Tsuda","doi":"10.1619/fesi.64.163","DOIUrl":"https://doi.org/10.1619/fesi.64.163","url":null,"abstract":"Time decay estimate of solutions to the compressible Navier-Stokes-Korteweg system is studied. Concerning the linearized problem, the decay estimate with diffusion wave property for an initial data is derived. As an application, the time decay estimate of solutions to the nonlinear problem is given. In contrast to the compressible Navier-Stokes system, for linear system regularities of the initial data are lower and independent of the order of derivative of solutions owing to smoothing effect from the Korteweg tensor. Furthermore, for the nonlinear system diffusion wave property is obtained with an initial data having lower regularity than that of study of the compressible Navier-Stokes system.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42950076","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
Connection Problem for the Generalized Hypergeometric Function 广义超几何函数的连接问题
IF 0.3 4区 数学
Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2019-04-05 DOI: 10.1619/fesi.64.323
Y. Matsuhira, H. Nagoya
{"title":"Connection Problem for the Generalized Hypergeometric Function","authors":"Y. Matsuhira, H. Nagoya","doi":"10.1619/fesi.64.323","DOIUrl":"https://doi.org/10.1619/fesi.64.323","url":null,"abstract":"We solve connection problem between fundamental solutions at singular points $0$ and $1$ for the generalized hypergeometric function, using analytic continuation of the integral representation. All connection coefficients are products of the sine and the cosecant.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43248286","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
Stability of Positive Solution to Fractional Logistic Equations 分数阶Logistic方程正解的稳定性
IF 0.3 4区 数学
Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2019-04-01 DOI: 10.1619/FESI.62.61
G. Dwivedi, J. Tyagi, R. B. Verma
{"title":"Stability of Positive Solution to Fractional Logistic Equations","authors":"G. Dwivedi, J. Tyagi, R. B. Verma","doi":"10.1619/FESI.62.61","DOIUrl":"https://doi.org/10.1619/FESI.62.61","url":null,"abstract":". In this paper, we show the existence of a classical solution to a class of fractional logistic equations in an open bounded subset with smooth boundary. We use the method of sub- and super-solutions with variational arguments to establish the existence of a unique positive solution. We also establish the stability and nondegeneracy of the positive solution.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1619/FESI.62.61","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43775975","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
Hopf Bifurcations for Neutral Functional Differential Equations with Infinite Delays 无穷时滞中立型泛函微分方程的Hopf分岔
IF 0.3 4区 数学
Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2019-01-01 DOI: 10.1619/FESI.62.95
Chuncheng Wang, Junjie Wei
{"title":"Hopf Bifurcations for Neutral Functional Differential Equations with Infinite Delays","authors":"Chuncheng Wang, Junjie Wei","doi":"10.1619/FESI.62.95","DOIUrl":"https://doi.org/10.1619/FESI.62.95","url":null,"abstract":"In the theory of linear autonomous neutral functional di¤erential equations with infinite delay, the spectrum distribution of the infinitesimal generator of its solution operators is studied under a certain phase space. Thereafter, we prove the representation theorem of the solution operators, which is later employed to obtain exponential dichotomy properties in terms of semigroup theory. Formal adjoint theory for linear autonomous NFDEs with infinite delay is established including such topics as formal adjoint equations, the relationship between the formal adjoint and true adjoint, and decomposing the phase space with formal adjoint equation. Finally, the algorithm for calculating the Hopf bifurcation properties for nonlinear NFDEs with infinite delay is presented based on the theory of linear equations.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1619/FESI.62.95","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67432124","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
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