Martin L. Kliemank, D. Wilde, Mario Bedrunka, A. Krämer, H. Foysi, D. Reith
{"title":"Assessment of lattice Boltzmann method for low-rise building wind flow simulation with limited resources","authors":"Martin L. Kliemank, D. Wilde, Mario Bedrunka, A. Krämer, H. Foysi, D. Reith","doi":"10.3934/dcdss.2023046","DOIUrl":"https://doi.org/10.3934/dcdss.2023046","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"171 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77495628","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":"Uniqueness of stationary distribution and exponential convergence for distribution dependent SDEs","authors":"Shao-Qin Zhang","doi":"10.3934/dcdss.2023003","DOIUrl":"https://doi.org/10.3934/dcdss.2023003","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"5 9 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76526629","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":"Concentration phenomenon for a fractional Schrödinger equation with discontinuous nonlinearity","authors":"V. Ambrosio","doi":"10.3934/dcdss.2023074","DOIUrl":"https://doi.org/10.3934/dcdss.2023074","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"151 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76856438","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":"Nonradial solutions for coupled elliptic system with critical exponent in exterior domain","authors":"Yuxia Guo, Dewei Li","doi":"10.3934/dcdss.2023099","DOIUrl":"https://doi.org/10.3934/dcdss.2023099","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"26 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86968739","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 two-relaxation-time collision operator in discrete kinetic theory models collisions between particles by grouping them into pairs with anti-parallel velocities. It prescribes a linear relaxation towards equilibrium with one rate for the even combination of distribution functions for each pair, and another rate for the odd combination. We reformulate this collision operator using relaxation rates for the forward-propagating and backward-propagating combinations instead. An optimal pair of relaxation rates sets the forward-propagating combination of each pair of distributions to equilibrium. Only the backward-propagating non-equilibrium distributions remain. Applying this result twice gives closed discrete equations for evolving the macroscopic variables alone across three time levels. We split the equivalent equations into a first-order system: a conservation law and a kinetic equation for the flux. All other quantities are evaluated at equilibrium. We apply this formalism to the magnetic field in a lattice Boltzmann scheme for magnetohydrodynamics. The antisymmetric part of the kinetic equation matches the Maxwell–Faraday equation and Ohm’s law. The symmetric part matches the hyperbolic divergence cleaning model. The discrete divergence of the magnetic field remains zero, to within round-off error, when the initial magnetic field is the discrete curl of a vector potential. We have thus constructed a mimetic or constrained transport scheme for magnetohydrodynamics.
{"title":"A magic two-relaxation-time lattice Boltzmann algorithm for magnetohydrodynamics","authors":"P. Dellar","doi":"10.3934/dcdss.2023157","DOIUrl":"https://doi.org/10.3934/dcdss.2023157","url":null,"abstract":". The two-relaxation-time collision operator in discrete kinetic theory models collisions between particles by grouping them into pairs with anti-parallel velocities. It prescribes a linear relaxation towards equilibrium with one rate for the even combination of distribution functions for each pair, and another rate for the odd combination. We reformulate this collision operator using relaxation rates for the forward-propagating and backward-propagating combinations instead. An optimal pair of relaxation rates sets the forward-propagating combination of each pair of distributions to equilibrium. Only the backward-propagating non-equilibrium distributions remain. Applying this result twice gives closed discrete equations for evolving the macroscopic variables alone across three time levels. We split the equivalent equations into a first-order system: a conservation law and a kinetic equation for the flux. All other quantities are evaluated at equilibrium. We apply this formalism to the magnetic field in a lattice Boltzmann scheme for magnetohydrodynamics. The antisymmetric part of the kinetic equation matches the Maxwell–Faraday equation and Ohm’s law. The symmetric part matches the hyperbolic divergence cleaning model. The discrete divergence of the magnetic field remains zero, to within round-off error, when the initial magnetic field is the discrete curl of a vector potential. We have thus constructed a mimetic or constrained transport scheme for magnetohydrodynamics.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"45 4 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85541214","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}
Sumit Kumar, Sandeep Sharma, A. Kashyap, Nitu Kumari, R. Agarwal
{"title":"Modelling the effect of environmental pollution on Zika outbreak: A case study of Brazil","authors":"Sumit Kumar, Sandeep Sharma, A. Kashyap, Nitu Kumari, R. Agarwal","doi":"10.3934/dcdss.2023048","DOIUrl":"https://doi.org/10.3934/dcdss.2023048","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"24 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74800708","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 note we prove uniqueness of the critical point for positive solutions of elliptic problems in bounded planar domains: we first examine the Poisson problem - Delta u = f(x,y) finding a geometric condition involving the curvature of the boundary and the normal derivative of f on the boundary to ensure uniqueness of the critical point. In the second part we consider stable solutions of the nonlinear problem -Delta u = f(u) in perturbation of convex domains.
{"title":"On the shape of solutions to elliptic equations in possibly non convex planar domains","authors":"Luca Battaglia, Fabio De Regibus, Massimo Grossi","doi":"10.3934/dcdss.2023194","DOIUrl":"https://doi.org/10.3934/dcdss.2023194","url":null,"abstract":"In this note we prove uniqueness of the critical point for positive solutions of elliptic problems in bounded planar domains: we first examine the Poisson problem - Delta u = f(x,y) finding a geometric condition involving the curvature of the boundary and the normal derivative of f on the boundary to ensure uniqueness of the critical point. In the second part we consider stable solutions of the nonlinear problem -Delta u = f(u) in perturbation of convex domains.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"265 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":"134980685","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 investigate the large-time behavior of bounded solutions of the Cauchy problem for a reaction-diffusion equation in $mathbb{R}^N$ with bistable reaction term. We consider initial conditions that are chiefly indicator functions of bounded Borel sets. We examine how geometric transformations of the supports of these initial conditions affect the propagation or extinction of the solutions at large time. We also consider two fragmentation indices defined in the set of bounded Borel sets and we establish some propagation or extinction results when the initial supports are weakly or highly fragmented. Lastly, we show that the large-time dynamics of the solutions is not monotone with respect to the considered fragmentation indices, even for equimeasurable sets.
{"title":"Propagation or extinction in bistable equations: The non-monotone role of initial fragmentation","authors":"Matthieu Alfaro, François Hamel, Lionel Roques","doi":"10.3934/dcdss.2023165","DOIUrl":"https://doi.org/10.3934/dcdss.2023165","url":null,"abstract":"In this paper, we investigate the large-time behavior of bounded solutions of the Cauchy problem for a reaction-diffusion equation in $mathbb{R}^N$ with bistable reaction term. We consider initial conditions that are chiefly indicator functions of bounded Borel sets. We examine how geometric transformations of the supports of these initial conditions affect the propagation or extinction of the solutions at large time. We also consider two fragmentation indices defined in the set of bounded Borel sets and we establish some propagation or extinction results when the initial supports are weakly or highly fragmented. Lastly, we show that the large-time dynamics of the solutions is not monotone with respect to the considered fragmentation indices, even for equimeasurable sets.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"35 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":"135400446","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 perform the apriori analysis of solutions to critical nonlinear elliptic equations on manifolds with boundary. The solutions are of minimizing type. The originality is that we impose no condition on the boundary, which leads us to assume $ L^2- $concentration. We also analyze the effect of a non-homogeneous nonlinearity that results in the fast convergence of the concentration point.
{"title":"Concentration analysis for elliptic critical equations with no boundary control: Ground-state blow-up","authors":"Hussein Mesmar, Frédéric Robert","doi":"10.3934/dcdss.2023199","DOIUrl":"https://doi.org/10.3934/dcdss.2023199","url":null,"abstract":"We perform the apriori analysis of solutions to critical nonlinear elliptic equations on manifolds with boundary. The solutions are of minimizing type. The originality is that we impose no condition on the boundary, which leads us to assume $ L^2- $concentration. We also analyze the effect of a non-homogeneous nonlinearity that results in the fast convergence of the concentration point.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"16 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":"135445015","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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