Journal of Dynamics and Differential Equations最新文献

{"title":"Second Order Splitting Dynamics with Vanishing Damping for Additively Structured Monotone Inclusions.","authors":"Radu Ioan Boţ, David Alexander Hulett","doi":"10.1007/s10884-022-10160-3","DOIUrl":"10.1007/s10884-022-10160-3","url":null,"abstract":"<p><p>In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator <i>A</i> and a cocoercive operator <i>B</i>. We study the asymptotic behaviour of the trajectories generated by a second order equation with vanishing damping, attached to this problem, and governed by a time-dependent forward-backward-type operator. This is a splitting system, as it only requires forward evaluations of <i>B</i> and backward evaluations of <i>A</i>. A proper tuning of the system parameters ensures the weak convergence of the trajectories to the set of zeros of <math><mrow><mi>A</mi><mo>+</mo><mi>B</mi></mrow></math>, as well as fast convergence of the velocities towards zero. A particular case of our system allows to derive fast convergence rates for the problem of minimizing the sum of a proper, convex and lower semicontinuous function and a smooth and convex function with Lipschitz continuous gradient. We illustrate the theoretical outcomes by numerical experiments.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10901952/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44794815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Oscillations in Planar Deficiency-One Mass-Action Systems.","authors":"Balázs Boros, Josef Hofbauer","doi":"10.1007/s10884-021-10051-z","DOIUrl":"10.1007/s10884-021-10051-z","url":null,"abstract":"<p><p>Whereas the positive equilibrium of a planar mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examples, with centers or multiple limit cycles.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10901957/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42713898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Stability Region for Schur Stable Trinomials with General Complex Coefficients","authors":"Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete","doi":"10.1007/s10884-023-10331-w","DOIUrl":"https://doi.org/10.1007/s10884-023-10331-w","url":null,"abstract":"<p>In this paper, we characterize the stability region for trinomials of the form <span>(f(zeta ):=azeta ^n + bzeta ^m +c)</span>, <span>(zeta in mathbb {C})</span>, where <i>a</i>, <i>b</i> and <i>c</i> are non-zero complex numbers and <span>(n,min mathbb {N})</span> with <span>(n&gt;m)</span>. More precisely, we provide necessary and sufficient conditions on the coefficients <i>a</i>, <i>b</i> and <i>c</i> in order that all the roots of the trinomial <i>f</i> belongs to the open unit disc in the complex plane. The proof is based on Bohl’s Theorem (Bohl in Math Ann 65(4):556–566, 1908) introduced in 1908.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138686974","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":"The Szymczak Functor and Shift Equivalence on the Category of Finite Sets and Finite Relations","authors":"Mateusz Przybylski, Marian Mrozek, Jim Wiseman","doi":"10.1007/s10884-023-10332-9","DOIUrl":"https://doi.org/10.1007/s10884-023-10332-9","url":null,"abstract":"<p>The construction of the Conley index for dynamical systems with discrete time requires an equivalence relation between morphisms induced on index pairs. It follows from the features of the Szymczak functor that shift equivalence, whose equivalence classes are the isomorphism classes in the Szymczak category, is the most general equivalence available. In the case of dynamics modeled from data, the morphisms induced on index pairs are relations. We present an algorithmizable classification of shift equivalence classes for the category of finite sets with arbitrary relations as morphisms. The research is the first step towards the construction of a Conley theory for relations.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138563435","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":"Hypocoercivity in Algebraically Constrained Partial Differential Equations with Application to Oseen Equations","authors":"Franz Achleitner, Anton Arnold, Volker Mehrmann","doi":"10.1007/s10884-023-10327-6","DOIUrl":"https://doi.org/10.1007/s10884-023-10327-6","url":null,"abstract":"<p>The long-time behavior of solutions to different versions of Oseen equations of fluid flow on the 2D torus is analyzed using the concept of hypocoercivity. The considered models are isotropic Oseen equations where the viscosity acts uniformly in all directions and anisotropic Oseen-type equations with different viscosity directions. The hypocoercivity index is determined (if it exists) and it is shown that similar to the finite dimensional case of ordinary differential equations and differential-algebraic equations it characterizes its decay behavior.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553371","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 the Failure of Linearization for Germs of $$C^1$$ Hyperbolic Vector Fields in Dimension One","authors":"Hélène Eynard-Bontemps, Andrés Navas","doi":"10.1007/s10884-023-10330-x","DOIUrl":"https://doi.org/10.1007/s10884-023-10330-x","url":null,"abstract":"<p>We investigate conjugacy classes of germs of hyperbolic 1-dimensional vector fields at the origin in low regularity. We show that the classical linearization theorem of Sternberg strongly fails in this setting by providing explicit uncountable families of mutually non-conjugate flows with the same multipliers, where conjugacy is considered in the bi-Lipschitz, <span>(C^1)</span> and <span>(C^{1+ac})</span> settings.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547649","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":"Center Stable Manifolds Around Line Solitary Waves of the Zakharov–Kuznetsov Equation","authors":"Yohei Yamazaki","doi":"10.1007/s10884-023-10329-4","DOIUrl":"https://doi.org/10.1007/s10884-023-10329-4","url":null,"abstract":"<p>In this paper, we construct center stable manifolds of unstable line solitary waves for the Zakharov–Kuznetsov equation on <span>({mathbb {R}} times {mathbb {T}}_L)</span> and show the orbital stability of the unstable line solitary waves on the center stable manifolds, which yields the asymptotic stability of unstable solitary waves on the center stable manifolds near by stable line solitary waves. The construction is based on the graph transform approach by Nakanishi and Schlag (SIAM J Math Anal 44:1175–1210, 2012). Applying the bilinear estimate on Fourier restriction spaces by Molinet and Pilod (Ann Inst H Poincaré Anal Non Lineaire 32:347–371, 2015) and modifying the mobile distance in Nakanishi and Schlag (2012), we construct a contraction map on the graph space.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524967","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":"Well-Posedness and Singularity Formation for the Kolmogorov Two-Equation Model of Turbulence in 1-D","authors":"Francesco Fanelli, Rafael Granero-Belinchón","doi":"10.1007/s10884-023-10326-7","DOIUrl":"https://doi.org/10.1007/s10884-023-10326-7","url":null,"abstract":"We study the Kolomogorov two-equation model of turbulence in one space dimension. Two are the main results of the paper. First of all, we establish a local well-posedness theory in Sobolev spaces even in the case of vanishing mean turbulent kinetic energy. Then, we show that there are smooth solutions which blow up in finite time. To the best of our knowledge, these results are the first establishing the well-posedness of the system for vanishing initial data and the occurence of finite time singularities for the model under study.","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135545535","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":"Dynamics of Interacting Monomial Scalar Field Potentials and Perfect Fluids","authors":"Artur Alho, Vitor Bessa, Filipe C. Mena","doi":"10.1007/s10884-023-10318-7","DOIUrl":"https://doi.org/10.1007/s10884-023-10318-7","url":null,"abstract":"Abstract Motivated by cosmological models of the early universe we analyse the dynamics of the Einstein equations with a minimally coupled scalar field with monomial potentials $$V(phi )=frac{(lambda phi )^{2n}}{2n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>V</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mfrac> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>λ</mml:mi> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> , $$lambda &gt;0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , $$nin {mathbb {N}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> , interacting with a perfect fluid with linear equation of state $$p_{textrm{pf}}=(gamma _{textrm{pf}}-1)rho _{textrm{pf}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mtext>pf</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>γ</mml:mi> <mml:mtext>pf</mml:mtext> </mml:msub> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>pf</mml:mtext> </mml:msub> </mml:mrow> </mml:math> , $$gamma _{textrm{pf}}in (0,2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>γ</mml:mi> <mml:mtext>pf</mml:mtext> </mml:msub> <mml:mo>∈</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , in flat Robertson–Walker spacetimes. The interaction is a friction-like term of the form $$Gamma (phi )=mu phi ^{2p}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>Γ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>μ</mml:mi> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , $$mu &gt;0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , $$pin {mathbb {N}}cup {0}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> <mml:mo>∪</mml:mo> <mml:mo>{</mml:mo> <mml:mn>0</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> . The analysis relies on the introduction of a new regular 3-dimensional dynamical systems’ formulation of the Einstein equations on a compact state space, and the use of dynamical systems’ tools such as qua","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135634809","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 weak/Strong Attractor for a 3-D Structural-Acoustic Interaction with Kirchhoff–Boussinesq Elastic Wall Subject to Restricted Boundary Dissipation","authors":"Irena Lasiecka, José H. Rodrigues","doi":"10.1007/s10884-023-10325-8","DOIUrl":"https://doi.org/10.1007/s10884-023-10325-8","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136159439","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}