{"title":"Large time behavior of solutions for a PDE model for compressible elastic curve","authors":"C. Kosugi, T. Aiki","doi":"10.3934/dcdss.2023161","DOIUrl":"https://doi.org/10.3934/dcdss.2023161","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"59 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91231318","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":"Nonexistence criteria for a generalized Boussinesq-type equation in bounded and unbounded domains","authors":"I. Aldawish, Ibtehal Alazman, M. Jleli, B. Samet","doi":"10.3934/dcdss.2023036","DOIUrl":"https://doi.org/10.3934/dcdss.2023036","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"17 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81840180","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":"Asset flow model for a homogeneous group of investors: High-frequency trading limit","authors":"D. Swigon","doi":"10.3934/dcdss.2023104","DOIUrl":"https://doi.org/10.3934/dcdss.2023104","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"2005 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88365362","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":"Potential well method for a class of fourth order wave equations with Newtonian potential","authors":"Ngo Tran Vu, Dao Bao Dung, M. Freitas","doi":"10.3934/dcdss.2023147","DOIUrl":"https://doi.org/10.3934/dcdss.2023147","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"18 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82693558","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 1D Burger's equation with Dirichlet boundary conditions exhibits a first transition from the trivial steady state to a sinusoidal patterned steady state as the parameter $ lambda $ which controls the linear term exceeds 1. The main goal of this paper is to present two different approaches regarding the transition of this patterned steady state. We believe that these approaches can be extended to study the dynamics of more interesting models. As a first approach, we consider an external forcing on the equation which supports a sinusoidal solution as a stable steady state which loses its stability at a critical threshold. We use the method of continued fractions to rigorously analyze the associated linear problem. In particular, we find that the system exhibits a mixed type transition with two distinct basins for initial conditions one of which leads to a local steady state and the other leaves a small neighborhood of the origin. As a second approach, we consider the dynamics on the center-unstable manifold of the first two modes of the unforced system. In this approach, the secondary transition produces two branches of steady state solutions. On one of these branches there is another transition which indicates a symmetry breaking phenomena.
{"title":"Two approaches to instability analysis of the viscous Burgers' equation","authors":"Messoud Efendiev, Taylan Sengul, Burhan Tiryakioglu","doi":"10.3934/dcdss.2023202","DOIUrl":"https://doi.org/10.3934/dcdss.2023202","url":null,"abstract":"The 1D Burger's equation with Dirichlet boundary conditions exhibits a first transition from the trivial steady state to a sinusoidal patterned steady state as the parameter $ lambda $ which controls the linear term exceeds 1. The main goal of this paper is to present two different approaches regarding the transition of this patterned steady state. We believe that these approaches can be extended to study the dynamics of more interesting models. As a first approach, we consider an external forcing on the equation which supports a sinusoidal solution as a stable steady state which loses its stability at a critical threshold. We use the method of continued fractions to rigorously analyze the associated linear problem. In particular, we find that the system exhibits a mixed type transition with two distinct basins for initial conditions one of which leads to a local steady state and the other leaves a small neighborhood of the origin. As a second approach, we consider the dynamics on the center-unstable manifold of the first two modes of the unforced system. In this approach, the secondary transition produces two branches of steady state solutions. On one of these branches there is another transition which indicates a symmetry breaking phenomena.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135506329","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}
Rashid Jan, S. Qureshi, S. Boulaaras, V. Pham, E. Hıncal, R. Guefaifia
{"title":"Optimization of the fractional-order parameter with the error analysis for human immunodeficiency virus under Caputo operator","authors":"Rashid Jan, S. Qureshi, S. Boulaaras, V. Pham, E. Hıncal, R. Guefaifia","doi":"10.3934/dcdss.2023010","DOIUrl":"https://doi.org/10.3934/dcdss.2023010","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"2677 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75685434","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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