Pub Date : 2024-02-06DOI: 10.1007/s10473-024-0219-7
Diana I. Hernández, Diego A. Rueda-Gómez, Élder J. Villamizar-Roa
In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝℕ, N = 2, 3. This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism. We prove the existence and uniqueness of weak-strong solutions, and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem, where the control is acting on the chemical signal. Posteriorly, we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory. Finally, we propose a discrete approximation scheme of the optimality system based on the gradient method, which is validated with some computational experiments.
{"title":"An optimal control problem for a Lotka-Volterra competition model with chemo-repulsion","authors":"Diana I. Hernández, Diego A. Rueda-Gómez, Élder J. Villamizar-Roa","doi":"10.1007/s10473-024-0219-7","DOIUrl":"https://doi.org/10.1007/s10473-024-0219-7","url":null,"abstract":"<p>In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ<sup>ℕ</sup>, <i>N</i> = 2, 3. This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism. We prove the existence and uniqueness of weak-strong solutions, and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem, where the control is acting on the chemical signal. Posteriorly, we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory. Finally, we propose a discrete approximation scheme of the optimality system based on the gradient method, which is validated with some computational experiments.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765632","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}
Pub Date : 2024-02-06DOI: 10.1007/s10473-024-0210-3
Yonghong Yao, Abubakar Adamu, Yekini Shehu
This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces. In our convergence analysis, we do not assume the on-line rule of the inertial parameters and the iterates, which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem. Consequently, our proof arguments are different from what is obtainable in the relevant literature. Finally, we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.
{"title":"Strongly convergent inertial forward-backward-forward algorithm without on-line rule for variational inequalities","authors":"Yonghong Yao, Abubakar Adamu, Yekini Shehu","doi":"10.1007/s10473-024-0210-3","DOIUrl":"https://doi.org/10.1007/s10473-024-0210-3","url":null,"abstract":"<p>This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces. In our convergence analysis, we do not assume the on-line rule of the inertial parameters and the iterates, which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem. Consequently, our proof arguments are different from what is obtainable in the relevant literature. Finally, we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"26 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765621","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}
Pub Date : 2024-02-06DOI: 10.1007/s10473-024-0209-9
Wenxian Ma, Sibei Yang
Let n ≥ 2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝn. In this article, we consider the weighted Kato square root problem for L. More precisely, we prove that the square root L1/2 satisfies the weighted Lp estimates (||{L^{1/2}}(f)|{|_{L_omega ^p({mathbb{R}^n})}} le C||nabla f|{|_{L_omega ^p({mathbb{R}^n};{mathbb{R}^n})}}) for any p ∈ (1, ∞) and ω ∈ Ap(ℝn) (the class of Muckenhoupt weights), and that (||nabla f|{|_{L_omega ^p({mathbb{R}^n};{mathbb{R}^n})}} le C||{L^{1/2}}(f)|{|_{L_omega ^p({mathbb{R}^n})}}) for any p ∈ (1, 2 + ε) and ω ∈ Ap(ℝn) ∩ (R{H_{({{2 + varepsilon } over p})prime }}({mathbb{R}^n})) (the class of reverse Hölder weights), where ε ∈ (0, ∞) is a constant depending only on n and the operator L, and where (({{2 + varepsilon } over p})prime ) denotes the Hölder conjugate exponent of ({{2 + varepsilon } over p}). Moreover, for any given q ∈ (2, ∞), we give a sufficient condition to obtain that (||nabla f|{|_{L_omega ^p({mathbb{R}^n};{mathbb{R}^n})}} le C||{L^{1/2}}(f)|{|_{L_omega ^p({mathbb{R}^n})}}) for any p ∈ (1, q) and (omega in {A_p}({mathbb{R}^n}) cap R{H_{({q over p})prime }}({mathbb{R}^n})). As an application, we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition, the Riesz transform ∇L−1/2 is bounded on Lpω(ℝn) for any given p ∈ (1, ∞) and ω ∈ Ap(ℝn). Furthermore, applications to the weighted L2-regularity problem with the Dirichlet or the Neumann boundary condition are also given.
设 n ≥ 2，设 L 为发散形式的二阶椭圆算子，其系数由 ℝn 中的椭圆对称部分和 BMO 反对称部分组成。更准确地说，我们证明平方根 L1/2 满足加权 Lp 估计值 (||{L^{1/2}}(f)|{{|{L_omega ^p({mathbb{R}^n})}}.|{L^{1/2}}(f)|{{L_omega ^p({/mathbb{R}^n})}}}；{对于任意 p∈ (1, ∞) 和 ω∈ Ap(ℝn)（Muckenhoupt 权重类），并且 (||nabla f|{|{_L_omega ^p({/mathbb{R}^n};{/mathbb{R}^n})}}})。对于任意 p∈ (1, 2 + ε) 且 ω∈ Ap(ℝn) ∩(R{H_{({{2 + varepsilon } over p})prime}}({/mathbb{R}^n})}（反向荷尔德权重类），|{{L^{1/2}}(f)|{|_{L_omega ^p({/mathbb{R}^n})}}(le C||{L^{1/2}}(f)|{|{{L_omega ^p({mathbb{R}^n})}})、其中 ε∈ (0, ∞) 是一个常数，只取决于 n 和算子 L，而 (({{2 + varepsilon } over p})prime ) 表示 ({{2 + varepsilon } over p}) 的霍尔德共轭指数。此外，对于任意给定的 q∈ (2, ∞)，我们给出了一个充分条件，即 (||nabla f|{|{L_omega ^p({mathbb{R}^n};{mathbb{R}^n})}})对于任意 p∈ (1, q) 并且 (omega in {A_p}({mathbb{R}^n}) cap R{H_{({q over p})prime }}({mathbb{R}^n})).作为应用，我们证明了当 L 中出现的系数矩阵 A 满足小 BMO 条件时，对于任意给定的 p∈ (1, ∞) 和 ω∈ Ap(ℝn) ，里兹变换 ∇L-1/2 在 Lpω(ℝn) 上是有界的。此外，还给出了迪里夏特或诺伊曼边界条件下加权 L2- 不规则性问题的应用。
{"title":"The weighted Kato square root problem of elliptic operators having a BMO anti-symmetric part","authors":"Wenxian Ma, Sibei Yang","doi":"10.1007/s10473-024-0209-9","DOIUrl":"https://doi.org/10.1007/s10473-024-0209-9","url":null,"abstract":"<p>Let <i>n</i> ≥ 2 and let <i>L</i> be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ<sup><i>n</i></sup>. In this article, we consider the weighted Kato square root problem for <i>L</i>. More precisely, we prove that the square root <i>L</i><sup>1/2</sup> satisfies the weighted <i>L</i><sup><i>p</i></sup> estimates <span>(||{L^{1/2}}(f)|{|_{L_omega ^p({mathbb{R}^n})}} le C||nabla f|{|_{L_omega ^p({mathbb{R}^n};{mathbb{R}^n})}})</span> for any <i>p</i> ∈ (1, ∞) and ω ∈ <i>A</i><sub><i>p</i></sub>(ℝ<sup><i>n</i></sup>) (the class of Muckenhoupt weights), and that <span>(||nabla f|{|_{L_omega ^p({mathbb{R}^n};{mathbb{R}^n})}} le C||{L^{1/2}}(f)|{|_{L_omega ^p({mathbb{R}^n})}})</span> for any p ∈ (1, 2 + <i>ε</i>) and <i>ω</i> ∈ <i>A</i><sub><i>p</i></sub>(ℝ<sup><i>n</i></sup>) ∩ <span>(R{H_{({{2 + varepsilon } over p})prime }}({mathbb{R}^n}))</span> (the class of reverse Hölder weights), where ε ∈ (0, ∞) is a constant depending only on <i>n</i> and the operator <i>L</i>, and where <span>(({{2 + varepsilon } over p})prime )</span> denotes the Hölder conjugate exponent of <span>({{2 + varepsilon } over p})</span>. Moreover, for any given <i>q</i> ∈ (2, ∞), we give a sufficient condition to obtain that <span>(||nabla f|{|_{L_omega ^p({mathbb{R}^n};{mathbb{R}^n})}} le C||{L^{1/2}}(f)|{|_{L_omega ^p({mathbb{R}^n})}})</span> for any <i>p</i> ∈ (1, <i>q</i>) and <span>(omega in {A_p}({mathbb{R}^n}) cap R{H_{({q over p})prime }}({mathbb{R}^n}))</span>. As an application, we prove that when the coefficient matrix A that appears in <i>L</i> satisfies the small BMO condition, the Riesz transform ∇<i>L</i><sup>−1/2</sup> is bounded on <i>L</i><span>\u0000<sup><i>p</i></sup><sub><i>ω</i></sub>\u0000</span><i>(</i>ℝ<sup><i>n</i></sup>) for any given <i>p</i> ∈ (1, ∞) and ω ∈ <i>A</i><sub><i>p</i></sub>(ℝ<sup><i>n</i></sup>). Furthermore, applications to the weighted <i>L</i><sup>2</sup>-regularity problem with the Dirichlet or the Neumann boundary condition are also given.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"80 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765639","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}
Pub Date : 2023-12-09DOI: 10.1007/s10473-024-0205-0
Lvqiao Liu, Juan Zeng
{"title":"The smoothing effect in sharp Gevrey space for the spatially homogeneous non-cutoff Boltzmann equations with a hard potential","authors":"Lvqiao Liu, Juan Zeng","doi":"10.1007/s10473-024-0205-0","DOIUrl":"https://doi.org/10.1007/s10473-024-0205-0","url":null,"abstract":"","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"11 17","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138585292","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}
Pub Date : 2023-12-09DOI: 10.1007/s10473-024-0203-2
Jian Chen
{"title":"On the Sobolev Dolbeault cohomology of a domain with pseudoconcave boundaries","authors":"Jian Chen","doi":"10.1007/s10473-024-0203-2","DOIUrl":"https://doi.org/10.1007/s10473-024-0203-2","url":null,"abstract":"","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"11 11","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138585297","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}
Pub Date : 2023-12-09DOI: 10.1007/s10473-024-0201-4
Ang Fu, Mingjin Li, Di Yang
{"title":"From wave functions to tau-functions for the Volterra lattice hierarchy","authors":"Ang Fu, Mingjin Li, Di Yang","doi":"10.1007/s10473-024-0201-4","DOIUrl":"https://doi.org/10.1007/s10473-024-0201-4","url":null,"abstract":"","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"3 7","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138585695","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}
Pub Date : 2023-11-29DOI: 10.1007/s10473-024-0116-0
Jieling Chen, Mingsheng Liu
In this paper, we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the form (L(f) = z{f_z} - bar z{f_{bar z}}), where f represents normalized harmonic mappings with bounded dilation. Then, using these results, we present better estimations for the Bloch constants of certain harmonic mappings L(f), where f is a K-quasiregular harmonic or open harmonic. Finally, we establish three versions of Bloch-Landau type theorem for biharmonic mappings of the form L(f). These results are sharp in some given cases and improve the related results of earlier authors.
本文首先得到了形式为(L(f) = z{f_z} - bar z{f_{bar z}})的调和映射的一元半径和Bloch常数的精确值，其中f表示有界膨胀的归一化调和映射。然后，利用这些结果，我们给出了某些调和映射L(f)的Bloch常数的更好估计，其中f是k -准正则调和或开调和。最后，我们建立了三种形式为L(f)的双调和映射的Bloch-Landau型定理。这些结果在某些特定情况下是尖锐的，并且改进了早期作者的相关结果。
{"title":"Estimate on the Bloch constant for certain harmonic mappings under a differential operator","authors":"Jieling Chen, Mingsheng Liu","doi":"10.1007/s10473-024-0116-0","DOIUrl":"10.1007/s10473-024-0116-0","url":null,"abstract":"<div><p>In this paper, we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the form <span>(L(f) = z{f_z} - bar z{f_{bar z}})</span>, where <i>f</i> represents normalized harmonic mappings with bounded dilation. Then, using these results, we present better estimations for the Bloch constants of certain harmonic mappings <i>L</i>(<i>f</i>), where <i>f</i> is a <i>K</i>-quasiregular harmonic or open harmonic. Finally, we establish three versions of Bloch-Landau type theorem for biharmonic mappings of the form <i>L</i>(<i>f</i>). These results are sharp in some given cases and improve the related results of earlier authors.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"295 - 310"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473088","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}
Pub Date : 2023-11-29DOI: 10.1007/s10473-024-0119-x
Ziheng Feng, Zhibo Huang, Yezhou Li
In this paper, we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order, and prove that the entire solutions are of infinite lower order. The properties on the radial distribution, the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.
{"title":"Entire solutions of higher order differential equations with entire coefficients having the same order","authors":"Ziheng Feng, Zhibo Huang, Yezhou Li","doi":"10.1007/s10473-024-0119-x","DOIUrl":"10.1007/s10473-024-0119-x","url":null,"abstract":"<div><p>In this paper, we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order, and prove that the entire solutions are of infinite lower order. The properties on the radial distribution, the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"355 - 368"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473256","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}
Pub Date : 2023-11-29DOI: 10.1007/s10473-024-0108-0
Xinling Liu, Kai Liu, Risto Korhonen, Galina Filipuk
This paper is devoted to considering the quasiperiodicity of complex differential polynomials, complex difference polynomials and complex delay-differential polynomials of certain types, and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.
{"title":"Quasiperiodicity of transcendental meromorphic functions","authors":"Xinling Liu, Kai Liu, Risto Korhonen, Galina Filipuk","doi":"10.1007/s10473-024-0108-0","DOIUrl":"10.1007/s10473-024-0108-0","url":null,"abstract":"<div><p>This paper is devoted to considering the quasiperiodicity of complex differential polynomials, complex difference polynomials and complex delay-differential polynomials of certain types, and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"161 - 172"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473075","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}
Pub Date : 2023-11-29DOI: 10.1007/s10473-024-0121-3
Wei Ding, Yan Tang, Yueping Zhu
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators, untill now, the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates. In this paper, we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
{"title":"The boundedness of operators on weighted multi-parameter local Hardy spaces","authors":"Wei Ding, Yan Tang, Yueping Zhu","doi":"10.1007/s10473-024-0121-3","DOIUrl":"10.1007/s10473-024-0121-3","url":null,"abstract":"<div><p>Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators, untill now, the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates. In this paper, we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"386 - 404"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473087","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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