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On Stationary Navier-Stokes Equations in the Upper-Half Plane 关于上半平面的静态纳维-斯托克斯方程
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-02-05 DOI: 10.1007/s10440-024-00636-3
Adrian D. Calderon, Van Le, Tuoc Phan
{"title":"On Stationary Navier-Stokes Equations in the Upper-Half Plane","authors":"Adrian D. Calderon,&nbsp;Van Le,&nbsp;Tuoc Phan","doi":"10.1007/s10440-024-00636-3","DOIUrl":"10.1007/s10440-024-00636-3","url":null,"abstract":"<div><p>We study the incompressible stationary Navier-Stokes equations in the upper-half plane with homogeneous Dirichlet boundary condition and non-zero external forcing terms. Existence of weak solutions is proved under a suitable condition on the external forces. Weak-strong uniqueness criteria based on various growth conditions at the infinity of weak solutions are also given. This is done by employing an energy estimate and a Hardy’s inequality. Several estimates of stream functions are carried out and two density lemmas with suitable weights for the homogeneous Sobolev space on 2-dimensional space are proved.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759235","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}
引用次数: 0
A Note on the Discrete Coagulation Equations with Collisional Breakage 关于碰撞破碎的离散凝固方程的说明
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-01-30 DOI: 10.1007/s10440-024-00634-5
Mashkoor Ali, Ankik Kumar Giri
{"title":"A Note on the Discrete Coagulation Equations with Collisional Breakage","authors":"Mashkoor Ali,&nbsp;Ankik Kumar Giri","doi":"10.1007/s10440-024-00634-5","DOIUrl":"10.1007/s10440-024-00634-5","url":null,"abstract":"<div><p>This article establishes the existence of global classical solutions to discrete coagulation equations with collisional breakage for collision kernels having linear growth. In contrast, the uniqueness is shown under additional restrictions on collision kernels. Moreover, mass conservation property and the positivity of solutions are also shown. While coagulation dominates, the occurrence of the gelation phenomenon for kernels having specific growth is also studied.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139589515","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}
引用次数: 0
Nonlinear Degenerate Parabolic Equations with a Singular Nonlinearity 具有奇异非线性的非线性退化抛物方程
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-01-30 DOI: 10.1007/s10440-024-00633-6
Hichem Khelifi, Fares Mokhtari
{"title":"Nonlinear Degenerate Parabolic Equations with a Singular Nonlinearity","authors":"Hichem Khelifi,&nbsp;Fares Mokhtari","doi":"10.1007/s10440-024-00633-6","DOIUrl":"10.1007/s10440-024-00633-6","url":null,"abstract":"<div><p>In this paper, we study the existence and regularity results for some parabolic equations with degenerate coercivity, and a singular right-hand side. The model problem is </p><div><div><span>$$ left { textstylebegin{array}{l@{quad }l} frac{partial u}{partial t}-text{div} left ( frac{left (1+vert nabla uvert ^{-Lambda }right )vert nabla uvert ^{p-2}nabla u}{(1+vert uvert )^{theta }} right )=frac{f}{(e^{u}-1)^{gamma }} &amp; text{in};;Q_{T}, u(x,0)=0 &amp; text{on};; Omega , u =0 &amp; text{on};; partial Q_{T}, end{array}displaystyle right . $$</span></div><div>\u0000 (0.1)\u0000 </div></div><p> where <span>(Omega )</span> is a bounded open subset of <span>(mathbb{R}^{N})</span> <span>(Ngeq 2)</span>, <span>(T&gt;0)</span>, <span>(Lambda in [0,p-1))</span>, <span>(f)</span> is a non-negative function belonging to <span>(L^{m}(Q_{T}))</span>, <span>(Q_{T}=Omega times (0,T))</span>, <span>(partial Q_{T}=partial Omega times (0,T))</span>, <span>(0leq theta &lt; p-1+frac{p}{N}+gamma (1+frac{p}{N}))</span> and <span>(0leq gamma &lt; p-1)</span>.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139589757","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}
引用次数: 0
Global Existence of Solutions to the Spherically Symmetric Einstein-Vlasov-Maxwell System 球对称爱因斯坦-弗拉索夫-麦克斯韦系统解的全局存在性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-01-24 DOI: 10.1007/s10440-024-00632-7
Timothée Raoul Moutngui Sée, Pierre Noundjeu
{"title":"Global Existence of Solutions to the Spherically Symmetric Einstein-Vlasov-Maxwell System","authors":"Timothée Raoul Moutngui Sée,&nbsp;Pierre Noundjeu","doi":"10.1007/s10440-024-00632-7","DOIUrl":"10.1007/s10440-024-00632-7","url":null,"abstract":"<div><p>We prove that the initial value problem with small data for the asymptotically flat spherically symmetric Einstein-Vlasov-Maxwell system admits the global in time solution in the case of the non-zero shift vector. This result extends the one already known for chargeless case.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139589764","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}
引用次数: 0
Nonuniform Sampling Theorem for Non-decaying Signals in Mixed-Norm Spaces (L_{vec{p},frac{1}{omega }}(mathbb{R}^{d})) 混合规范空间中非衰减信号的非均匀采样定理 $L_{vec{p},frac{1}{omega }}(mathbb{R}^{d})$
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-01-11 DOI: 10.1007/s10440-023-00631-0
Junjian Zhao
{"title":"Nonuniform Sampling Theorem for Non-decaying Signals in Mixed-Norm Spaces (L_{vec{p},frac{1}{omega }}(mathbb{R}^{d}))","authors":"Junjian Zhao","doi":"10.1007/s10440-023-00631-0","DOIUrl":"10.1007/s10440-023-00631-0","url":null,"abstract":"<div><p>In this paper, combining the non-decaying properties with the mixed-norm properties, the revelent sampling problems are studied under the target space of <span>(L_{vec{p},frac{1}{omega }}(mathbb{R}^{d}))</span>. Firstly, we will give a stability theorem for the shift-invariant subspace <span>(V_{vec{p},frac{1}{omega }}(varphi ))</span>. Secondly, an ideal sampling in <span>(W_{vec{p},frac{1}{omega }}^{s}(mathbb{R}^{d}))</span> is proved, and thirdly, a convergence theorem (or algorithm) is shown for <span>(V_{vec{p},frac{1}{omega }}(varphi ))</span>. It should be pointed out that the auxiliary function <span>(varphi )</span> enjoys the membership in a Wiener amalgam space.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139423798","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}
引用次数: 0
Mathematical Scrutiny of Singular Predator-Prey Model with Stage-Structure of Prey 具有猎物阶段性结构的奇异捕食者-猎物模型的数学审视
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-01-11 DOI: 10.1007/s10440-023-00630-1
U. Yadav, A. K. Nayak, S. Gakkhar
{"title":"Mathematical Scrutiny of Singular Predator-Prey Model with Stage-Structure of Prey","authors":"U. Yadav,&nbsp;A. K. Nayak,&nbsp;S. Gakkhar","doi":"10.1007/s10440-023-00630-1","DOIUrl":"10.1007/s10440-023-00630-1","url":null,"abstract":"<div><p>In this paper, a stage structured predator-prey model with Holling type II functional response is formulated, considering the juvenile prey as the favorite food for the generalist predator. Further, the existence of predators is ensured by the sufficient amount of alternative food available in the habitat. The proportional harvesting of the adult prey is incorporated with the assumption that only the adult prey are of economic worth. The existence and local stability of the distinct equilibrium points of the system are investigated. The bifurcation from origin to predator free equilibrium state is obtained for the bifurcation parameter-effort on harvesting. The occurrence of Hopf bifurcation about the interior equilibrium state is established for arbitrary model parameters and the supercritical nature of this bifurcation is proved by fixing these parametric values. An algebraic equation is included to this modified model to analyze the economic benefits resulted from the harvesting of adult prey. The singularity-induced bifurcation (SIB) about the coexisting equilibrium state of differential-algebraic system is deduced along the parameter <span>(v)</span> at <span>(v=0)</span>, <span>(v)</span> being the profit/loss due to harvesting. The state feedback controller is recommended to eliminate the SIB about the coexisting equilibrium state for the differential algebraic system. Adopting an appropriate feedback control would ensure the stability of co-existence interior equilibrium state along with economic profit from harvesting. Numerical examples are used to elaborate the analytical results obtained.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139420610","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}
引用次数: 0
Exterior Boundary-Value Poincaré Problem for Elliptic Systems of the Second Order with Two Independent Variables 具有两个独立变量的二阶椭圆系统的外部边值泊恩卡雷问题
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-12-21 DOI: 10.1007/s10440-023-00629-8
F. Criado-Aldeanueva, N. Odishelidze, J. M. Sanchez, M. Khachidze
{"title":"Exterior Boundary-Value Poincaré Problem for Elliptic Systems of the Second Order with Two Independent Variables","authors":"F. Criado-Aldeanueva,&nbsp;N. Odishelidze,&nbsp;J. M. Sanchez,&nbsp;M. Khachidze","doi":"10.1007/s10440-023-00629-8","DOIUrl":"10.1007/s10440-023-00629-8","url":null,"abstract":"<div><p>This paper offers a number of examples showing that in the case of two independent variables the uniform ellipticity of a linear system of differential equations with partial derivatives of the second order, which fulfills condition (3), do not always cause the normal solvability of formulated exterior elliptic problems in the sense of Noether.</p><p>Nevertheless, from the system of differential equations with partial derivatives of elliptic type it is possible to choose, under certain additional conditions, classes which are normally solvable in the sense of Noether.</p><p>This paper also shows that for the so-called decomposed system of differential equations, with partial derivatives of an elliptic type in the case of exterior regions, the Noether theorems are valid.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-023-00629-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138952305","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}
引用次数: 0
Topological Travelling Waves of a Macroscopic Swarmalator Model in Confined Geometries 封闭几何中宏观蜂群模型的拓扑游波
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-12-14 DOI: 10.1007/s10440-023-00628-9
P. Degond, A. Diez
{"title":"Topological Travelling Waves of a Macroscopic Swarmalator Model in Confined Geometries","authors":"P. Degond,&nbsp;A. Diez","doi":"10.1007/s10440-023-00628-9","DOIUrl":"10.1007/s10440-023-00628-9","url":null,"abstract":"<div><p>We investigate a new class of topological travelling-wave solutions for a macroscopic swarmalator model involving force non-reciprocity. Swarmalators are systems of self-propelled particles endowed with a phase variable. The particles are subject to coupled swarming and synchronization. In previous work, the swarmalator under study was introduced, the macroscopic model was derived and doubly periodic travelling-wave solutions were exhibited. Here, we focus on the macroscopic model and investigate new classes of two-dimensional travelling-wave solutions. These solutions are confined in a strip or in an annulus. In the case of the strip, they are periodic along the strip direction. Both of them have non-trivial topology as their phases increase by a multiple of <span>(2 pi )</span> from one period (in the case of the strip) or one revolution (in the case of the annulus) to the next. Existence and qualitative behavior of these solutions are investigated.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138634004","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}
引用次数: 0
Symmetry of Positive Solutions for Lane-Emden Systems Involving the Logarithmic Laplacian 涉及对数拉普拉卡方的 Lane-Emden 系统正解的对称性
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-12-12 DOI: 10.1007/s10440-023-00627-w
Rong Zhang, Vishvesh Kumar, Michael Ruzhansky
{"title":"Symmetry of Positive Solutions for Lane-Emden Systems Involving the Logarithmic Laplacian","authors":"Rong Zhang,&nbsp;Vishvesh Kumar,&nbsp;Michael Ruzhansky","doi":"10.1007/s10440-023-00627-w","DOIUrl":"10.1007/s10440-023-00627-w","url":null,"abstract":"<div><p>We study the Lane-Emden system involving the logarithmic Laplacian: </p><div><div><span>$$ textstylebegin{cases} mathcal{L}_{Delta }u(x)=v^{p}(x) ,&amp; xin mathbb{R}^{n}, mathcal{L}_{Delta }v(x)=u^{q}(x) ,&amp; xin mathbb{R}^{n}, end{cases} $$</span></div></div><p> where <span>(p,q&gt;1)</span>, <span>(ngeq 2)</span> and <span>(mathcal{L}_{Delta })</span> denotes the logarithmic Laplacian arising as a formal derivative <span>(partial _{s}|_{s=0}(-Delta )^{s})</span> of the fractional Laplacian <span>((-Delta )^{s})</span> at <span>(s=0)</span>. By using a direct method of moving planes for the logarithmic Laplacian, we obtain the symmetry and monotonicity of the positive solutions to the Lane-Emden system. We also establish some key ingredients needed in order to apply the method of moving planes such as the maximum principle for anti-symmetric functions, the narrow region principle, and decay at infinity. Further, we discuss such results for a generalized system of the Lane-Emden type involving the logarithmic Laplacian.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138573349","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}
引用次数: 0
Boundary Controllability of a Simplified Stabilized Kuramoto-Sivashinsky System 简化的库拉莫托-西瓦申斯基稳定系统的边界可控性
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-12-12 DOI: 10.1007/s10440-023-00626-x
Víctor Hernández-Santamaría, Alberto Mercado, Piero Visconti
{"title":"Boundary Controllability of a Simplified Stabilized Kuramoto-Sivashinsky System","authors":"Víctor Hernández-Santamaría,&nbsp;Alberto Mercado,&nbsp;Piero Visconti","doi":"10.1007/s10440-023-00626-x","DOIUrl":"10.1007/s10440-023-00626-x","url":null,"abstract":"<div><p>In this paper, we study the controllability of a nonlinear system of coupled second- and fourth-order parabolic equations. This system can be regarded as a simplification of the well-known stabilized Kuramoto-Sivashinsky system. Using only one control applied on the boundary of the second-order equation, we prove that the local-null controllability of the system holds if the square root of the diffusion coefficient of the second-order equation is an irrational number with finite Liouville-Roth constant.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138578056","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}
引用次数: 0
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