. It is considered the mathematical model of a benchmark hydroe-lectric power plant containing a water reservoir (lake), two water conduits (the tunnel and the turbine penstock), the surge tank and the hydraulic turbine; all distributed (Darcy-Weisbach) and local hydraulic losses are neglected,the only energy dissipator remains the throttling of the surge tank. Exponential stability would require asymptotic stability of the difference operator associated to the model. However in this case this stability is “fragile” i
{"title":"Around certain critical cases in stability studies in hydraulic engineering","authors":"V. Rǎsvan","doi":"10.5817/am2023-1-109","DOIUrl":"https://doi.org/10.5817/am2023-1-109","url":null,"abstract":". It is considered the mathematical model of a benchmark hydroe-lectric power plant containing a water reservoir (lake), two water conduits (the tunnel and the turbine penstock), the surge tank and the hydraulic turbine; all distributed (Darcy-Weisbach) and local hydraulic losses are neglected,the only energy dissipator remains the throttling of the surge tank. Exponential stability would require asymptotic stability of the difference operator associated to the model. However in this case this stability is “fragile” i","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"50 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75748614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. This paper deals with the oscillation problems on the nonlinear differential equation ( a ( t ) | x 0 | p ( t ) − 2 x 0 ) 0 + b ( t ) | x | λ − 2 x = 0 involving p ( t )-Laplacian. Sufficient conditions are given under which all proper solutions are oscillatory. In addition, we give a-priori estimates for nonoscillatory solutions and propose an open problem.
． 研究了p (t)-拉普拉斯算子的非线性微分方程(a (t) | x 0 | p (t)−2 x 0) 0 + b (t) | x | λ−2 x = 0的振动问题。给出了所有固有解都是振荡解的充分条件。此外，我们给出了非振荡解的先验估计，并提出了一个开放问题。
{"title":"A note on the oscillation problems for differential equations with $p(t)$-Laplacian","authors":"K. Fujimoto","doi":"10.5817/am2023-1-39","DOIUrl":"https://doi.org/10.5817/am2023-1-39","url":null,"abstract":". This paper deals with the oscillation problems on the nonlinear differential equation ( a ( t ) | x 0 | p ( t ) − 2 x 0 ) 0 + b ( t ) | x | λ − 2 x = 0 involving p ( t )-Laplacian. Sufficient conditions are given under which all proper solutions are oscillatory. In addition, we give a-priori estimates for nonoscillatory solutions and propose an open problem.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"101 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72410688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Padovan and Perrin numbers as products of two generalized Lucas numbers","authors":"K. N. Adédji, Japhet Odjoumani, A. Togbé","doi":"10.5817/am2023-4-315","DOIUrl":"https://doi.org/10.5817/am2023-4-315","url":null,"abstract":"","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81746120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system.
{"title":"Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems","authors":"Sachiko Ishida, T. Yokota","doi":"10.5817/am2023-2-181","DOIUrl":"https://doi.org/10.5817/am2023-2-181","url":null,"abstract":". This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"120 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87837918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. The work deals with non-Markov processes and the construction of systems of differential equations with delay that describe the probability vectors of such processes. The generating stochastic operator and properties of stochastic operators are used to construct systems that define non-Markov processes.
{"title":"Systems of differential equations modeling non-Markov processes","authors":"I. Dzhalladova, M. Ruzicková","doi":"10.5817/am2023-1-21","DOIUrl":"https://doi.org/10.5817/am2023-1-21","url":null,"abstract":". The work deals with non-Markov processes and the construction of systems of differential equations with delay that describe the probability vectors of such processes. The generating stochastic operator and properties of stochastic operators are used to construct systems that define non-Markov processes.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90179568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been proved. The purpose of this paper is to derive boundedness and stabilization in the parabolic-parabolic-elliptic version.
{"title":"Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system","authors":"Yutaro Chiyo","doi":"10.5817/am2023-2-163","DOIUrl":"https://doi.org/10.5817/am2023-2-163","url":null,"abstract":". This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been proved. The purpose of this paper is to derive boundedness and stabilization in the parabolic-parabolic-elliptic version.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"102 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83062033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. This paper deals with existence of finite-time blow-up solutions to a degenerate parabolic–elliptic Keller–Segel system with logistic source. Recently, finite-time blow-up was established for a degenerate Jäger–Luckhaus system with logistic source. However, blow-up solutions of the aforementioned system have not been obtained. The purpose of this paper is to construct blow-up solutions of a degenerate Keller–Segel system with logistic source.
{"title":"Existence of blow-up solutions for a degenerate parabolic-elliptic Keller–Segel system with logistic source","authors":"Yuya Tanaka","doi":"10.5817/am2023-2-223","DOIUrl":"https://doi.org/10.5817/am2023-2-223","url":null,"abstract":". This paper deals with existence of finite-time blow-up solutions to a degenerate parabolic–elliptic Keller–Segel system with logistic source. Recently, finite-time blow-up was established for a degenerate Jäger–Luckhaus system with logistic source. However, blow-up solutions of the aforementioned system have not been obtained. The purpose of this paper is to construct blow-up solutions of a degenerate Keller–Segel system with logistic source.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"30 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82265519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We show the location of so called critical points , i.e., couples of diffusion coefficients for which a non-trivial solution of a linear reaction-diffusion system of activator-inhibitor type on an interval with Neumann boundary conditions and with additional non-linear unilateral condition at one or two points on the boundary and/or in the interior exists. Simultaneously, we show the profile of such solutions.
{"title":"Critical points for reaction-diffusion system with one and two unilateral conditions","authors":"Jan Eisner, Jan Žilavý","doi":"10.5817/am2023-2-173","DOIUrl":"https://doi.org/10.5817/am2023-2-173","url":null,"abstract":". We show the location of so called critical points , i.e., couples of diffusion coefficients for which a non-trivial solution of a linear reaction-diffusion system of activator-inhibitor type on an interval with Neumann boundary conditions and with additional non-linear unilateral condition at one or two points on the boundary and/or in the interior exists. Simultaneously, we show the profile of such solutions.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80925405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. The paper considers a scalar differential equation of an advance-delay type
． 研究一类超前-时滞型标量微分方程
{"title":"Solutions of an advance-delay differential equation and their asymptotic behaviour","authors":"G. Vážanová","doi":"10.5817/am2023-1-141","DOIUrl":"https://doi.org/10.5817/am2023-1-141","url":null,"abstract":". The paper considers a scalar differential equation of an advance-delay type","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83226100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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