{"title":"Dynamics of a competition model with intra- and interspecific interference in the unstirred chemostat","authors":"Lin Wang, Jianhua Wu","doi":"10.3934/dcdss.2023098","DOIUrl":"https://doi.org/10.3934/dcdss.2023098","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"301 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78904336","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":"On nonlinear multipoint conjugate value problem for feedback control systems in the cone","authors":"N. Huy, Nguyen Dang Quang, Vo Viet Tri","doi":"10.3934/dcdss.2023126","DOIUrl":"https://doi.org/10.3934/dcdss.2023126","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"241 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76767347","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":"Analytical and numerical study of a nonlinear Volterra integro-differential equation with the Caputo-Fabrizio fractional derivative","authors":"M. Bekkouche, A. Ahmed, F. Yazid, F.S. Djeradi","doi":"10.3934/dcdss.2023040","DOIUrl":"https://doi.org/10.3934/dcdss.2023040","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"211 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77502916","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":"Asymptotic stability and the hair-trigger effect in Cauchy problem of the parabolic-parabolic Keller-Segel system with logistic source","authors":"De-Ji-Xiang-Mao, Jing Li, Jingxue Yin","doi":"10.3934/dcdss.2023092","DOIUrl":"https://doi.org/10.3934/dcdss.2023092","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"10 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78363948","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":"On initial value problem for diffusion equation with Caputo-Fabrizio operator on the plane","authors":"Vo Ngoc Minh, Le Dinh Long","doi":"10.3934/dcdss.2023196","DOIUrl":"https://doi.org/10.3934/dcdss.2023196","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"307 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":"134884474","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 problem begin{equation} label{bn} -Delta u=|u|^{4over n-2}u+lambda V u hbox{in} Omega, u=0 hbox{on} partialOmega end{equation} where $Omega$ is a bounded regular domain in $mathbb R^n$, $lambdain mathbb R$ and $Vin C^0(overline Omega),$ that was introduced by Brezis and Nirenberg in their famous paper, where they address the existence of positive solutions in the autonomous case, i.e. the potential $V$ is constant. Since then, a huge amount of work has been done. In the following we will make a brief history highlighting the results which are much closer to the problem we wish to study in the present paper.
{"title":"The Brezis-Nirenberg problem in 4D","authors":"Angela Pistoia, Serena Rocci","doi":"10.3934/dcdss.2023191","DOIUrl":"https://doi.org/10.3934/dcdss.2023191","url":null,"abstract":"The problem begin{equation} label{bn} -Delta u=|u|^{4over n-2}u+lambda V u hbox{in} Omega, u=0 hbox{on} partialOmega end{equation} where $Omega$ is a bounded regular domain in $mathbb R^n$, $lambdain mathbb R$ and $Vin C^0(overline Omega),$ that was introduced by Brezis and Nirenberg in their famous paper, where they address the existence of positive solutions in the autonomous case, i.e. the potential $V$ is constant. Since then, a huge amount of work has been done. In the following we will make a brief history highlighting the results which are much closer to the problem we wish to study in the present paper.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"9 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":"135010045","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}
Nikos I. Kavallaris, Christos V. Nikolopoulos, Athanasios N. Yannacopoulos
In this paper, we study a stochastic parabolic problem involving a nonlocal diffusion operator associated with nonlocal Robin-type boundary conditions. The stochastic dynamics under consideration is driven by a mixture of a classical Brownian and a fractional Brownian motion with Hurst index $ Hin(frac{1}{2}, 1). $ We first establish local in time existence results and then explore conditions under which the resulting SPDE exhibits finite-time quenching. Using results on the probability distribution of perpetual integral functionals of Brownian motion as well as tail estimates for the fractional Brownian motion we provide analytic estimates for certain quantities of interest, such as upper bounds for quenching times and the corresponding quenching probabilities. The existence of global in time solutions is also investigated and as a consequence a lower estimate of the quenching time is also derived. Our analytical results demonstrate the non-trivial impact of the noise on the dynamics of the system. The analytic results are complemented with a detailed numerical study of the model under Dirichlet boundary conditions. A possible application concerning MEMS technology is considered and the implications of the results in this context are commented upon.
{"title":"On the impact of noise on quenching for a nonlocal diffusion model driven by a mixture of Brownian and fractional Brownian motions","authors":"Nikos I. Kavallaris, Christos V. Nikolopoulos, Athanasios N. Yannacopoulos","doi":"10.3934/dcdss.2023192","DOIUrl":"https://doi.org/10.3934/dcdss.2023192","url":null,"abstract":"In this paper, we study a stochastic parabolic problem involving a nonlocal diffusion operator associated with nonlocal Robin-type boundary conditions. The stochastic dynamics under consideration is driven by a mixture of a classical Brownian and a fractional Brownian motion with Hurst index $ Hin(frac{1}{2}, 1). $ We first establish local in time existence results and then explore conditions under which the resulting SPDE exhibits finite-time quenching. Using results on the probability distribution of perpetual integral functionals of Brownian motion as well as tail estimates for the fractional Brownian motion we provide analytic estimates for certain quantities of interest, such as upper bounds for quenching times and the corresponding quenching probabilities. The existence of global in time solutions is also investigated and as a consequence a lower estimate of the quenching time is also derived. Our analytical results demonstrate the non-trivial impact of the noise on the dynamics of the system. The analytic results are complemented with a detailed numerical study of the model under Dirichlet boundary conditions. A possible application concerning MEMS technology is considered and the implications of the results in this context are commented upon.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"153 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":"135213415","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}
A standard elasto-plasto-dynamic model at finite strains based on the Lie-Liu-Kröner multiplicative decomposition, formulated in rates, is here enhanced to cope with spatially inhomogeneous materials by using the reference (called also return) mapping. Also an isotropic hardening can be involved. Consistent thermodynamics is formulated, allowing for both the free and the dissipation energies temperature dependent. The model complies with the energy balance and entropy inequality. A multipolar Stokes-like viscosity and plastic rate gradient are used to allow for a rigorous analysis towards existence of weak solutions by a semi-Galerkin approximation.
{"title":"Inhomogeneous finitely-strained thermoplasticity with hardening by an Eulerian approach","authors":"Tomáš Roubíček, Giuseppe Tomassetti","doi":"10.3934/dcdss.2023180","DOIUrl":"https://doi.org/10.3934/dcdss.2023180","url":null,"abstract":"A standard elasto-plasto-dynamic model at finite strains based on the Lie-Liu-Kröner multiplicative decomposition, formulated in rates, is here enhanced to cope with spatially inhomogeneous materials by using the reference (called also return) mapping. Also an isotropic hardening can be involved. Consistent thermodynamics is formulated, allowing for both the free and the dissipation energies temperature dependent. The model complies with the energy balance and entropy inequality. A multipolar Stokes-like viscosity and plastic rate gradient are used to allow for a rigorous analysis towards existence of weak solutions by a semi-Galerkin approximation.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"2011 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":"136256737","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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