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Evolution and interaction of δ-waves in the zero-pressure gas dynamics system 零压气体动力学系统中δ波的演变和相互作用
IF 1 4区 数学 Q1 MATHEMATICS Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0510-7
Abhishek Das, K. T. Joseph

Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system. In this paper, we study the initial value problem for one dimensional zero-pressure gas dynamics system. Here the first equation is the Burgers equation and the second one is the continuity equation. We consider the solution with initial data in the space of bounded Borel measures. First we prove a general existence result in the algebra of generalized functions of Colombeau. Then we study in detail special solutions with δ-measures as initial data. We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves. This gives an understanding of plane-wave interactions in the multidimensional case. We use the vanishing viscosity method in our analysis as this gives the physical solution.

多维零压气体动力学系统平面波的演变和相互作用导致了对相应一维系统的研究。本文研究一维零压气体动力学系统的初值问题。这里的第一个方程是布尔格斯方程,第二个方程是连续性方程。我们考虑的是有界 Borel 量空间中初始数据的解。首先,我们证明了科伦坡广义函数代数中的一般存在性结果。然后,我们详细研究以 δ 量作为初始数据的特殊解。我们研究了源于集中在两个点源上的初始数据的波的相互作用,以及与经典冲击波/反射波的相互作用。这有助于理解多维情况下的平面波相互作用。我们在分析中使用了粘性消失法,因为它给出了物理解决方案。
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引用次数: 0
The global existence and uniqueness of smooth solutions to a fluid-particle interaction model in the flowing regime 流体-粒子相互作用模型流态平稳解的全局存在性和唯一性
IF 1 4区 数学 Q1 MATHEMATICS Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0513-4
Lin Zheng, Shu Wang

This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime in ℝ3. Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces, the existence and uniqueness of global smooth solutions in H3 of the system are established by using the careful energy method.

本文关注的是ℝ3 中所谓流动体系中三维流体-粒子相互作用模型的 Cauchy 问题。在一些 Sobolev 空间中,在外部势和静止解的初始扰动都很小的假设下,利用谨慎能量法建立了系统在 H3 中全局光滑解的存在性和唯一性。
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引用次数: 0
Toeplitz determinants in one and higher dimensions 一维及更高维度的托普利兹行列式
IF 1 4区 数学 Q1 MATHEMATICS Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0517-0
Surya Giri, S. Sivaprasad Kumar

In this study, we derive the sharp bounds of certain Toeplitz determinants whose entries are the coefficients of holomorphic functions belonging to a class defined on the unit disk (mathbb{U}). Furthermore, these results are extended to a class of holomorphic functions on the unit ball in a complex Banach space and on the unit polydisc in ℂn. The obtained results provide the bounds of Toeplitz determinants in higher dimensions for various subclasses of normalized univalent functions.

在本研究中,我们推导了某些托普利兹行列式的尖锐边界,这些行列式的项是属于定义在单位圆盘 (mathbb{U})上的一类全纯函数的系数。此外,这些结果还扩展到了复巴纳赫空间中单位球和ℂn 中单位多圆盘上的一类全纯函数。所得到的结果为各种归一化等价函数子类提供了更高维度的托普利兹行列式的边界。
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引用次数: 0
Global unique solutions for the incompressible MHD equations with variable density and electrical conductivity 密度和导电率可变的不可压缩多流体力学方程的全局唯一解
IF 1 4区 数学 Q1 MATHEMATICS Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0507-2
Xueli Ke

We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations, with the initial data (u0, B0) being located in the critical Besov space (dot{B}_{p,1}^{{-1}+{{2}over{p}}}(mathbb{R}^{2})) (1 < p < 2) and the initial density ρ0 being close to a positive constant. By using weighted global estimates, maximal regularity estimates in the Lorentz space for the Stokes system, and the Lagrangian approach, we show that the 2-D MHD equations have a unique global solution.

我们研究了二维非均质不可压缩 MHD 方程的全局唯一解,初始数据 (u0, B0) 位于临界贝索夫空间 (dot{B}_{p,1}^{{-1}+{{2}over{p}}}(mathbb{R}^{2})) (1 < p < 2),初始密度 ρ0 接近正常数。通过使用加权全局估计、斯托克斯系统洛伦兹空间中的最大正则估计以及拉格朗日方法,我们证明了二维 MHD 方程具有唯一的全局解。
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引用次数: 0
Normalized solutions for the general Kirchhoff type equations 一般基尔霍夫方程的归一化解法
IF 1 4区 数学 Q1 MATHEMATICS Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0514-3
Wenmin Liu, Xuexiu Zhong, Jinfang Zhou

In the present paper, we prove the existence, non-existence and multiplicity of positive normalized solutions (λc, uc) ∈ ℝ × H1 (ℝN) to the general Kirchhoff problem

$$-Mleft(int_{mathbb{R}^N}vertnabla uvert^2 {rm d}xright)Delta u +lambda u=g(u)~hbox{in}~mathbb{R}^N, uin H^1(mathbb{R}^N),Ngeq 1,$$

satisfying the normalization constraint (int_{mathbb{R}^N}u^2{rm d}x=c), where MC([0, ∞)) is a given function satisfying some suitable assumptions. Our argument is not by the classical variational method, but by a global branch approach developed by Jeanjean et al. [J Math Pures Appl, 2024, 183: 44–75] and a direct correspondence, so we can handle in a unified way the nonlinearities g(s), which are either mass subcritical, mass critical or mass supercritical.

在本文中,我们证明了一般基尔霍夫问题$$-Mleft(int_{) 的正规范化解 (λc、uc) ∈ ℝ × H1 (ℝN) to the general Kirchhoff problem$$-Mleft(int_{mathbb{R}^N}vertnabla uvert^2 {rm d}xright)Delta u +lambda u=g(u)~hbox{in}~mathbb{R}^N、uin H^1(mathbb{R}^N),Ngeq 1,$$满足归一化约束条件((int_mathbb{R}^N}u^^2{rm d}x=c),其中 M∈ C([0, ∞))是一个满足一些合适假设的给定函数。我们的论证不是通过经典的变分法,而是通过 Jeanjean 等人开发的全局分支法[J Math Pures Appl, 2024, 183: 44-75]和直接对应法,因此我们可以统一处理非线性 g(s),即质量次临界、质量临界或质量超临界。
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引用次数: 0
Big Hankel operators on Hardy spaces of strongly pseudoconvex domains 强伪凸域哈代空间上的大汉克尔算子
IF 1 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-01 DOI: 10.1007/s10473-024-0301-1

Abstract

In this article, we investigate the (big) Hankel operator Hf on the Hardy spaces of bounded strongly pseudoconvex domains Ω in ℂn. We observe that Hf is bounded on Hp (Ω) (1 < p < ∞) if f belongs to BMO and we obtain some characterizations for Hf on H2 (Ω) of other pseudoconvex domains. In these arguments, Amar’s Lp-estimations and Berndtsson’s L2-estimations for solutions of the ({{bar partial }_b}) -equation play a crucial role. In addition, we solve Gleason’s problem for Hardy spaces Hp(Ω) (1 ≤ p ≤ ∞) of bounded strongly pseudoconvex domains.

摘要 本文研究ℂn 中有界强伪凸域 Ω 的哈代空间上的(大)汉克尔算子 Hf。我们观察到,如果 f 属于 BMO,则 Hf 在 Hp (Ω) (1 < p < ∞) 上是有界的。在这些论证中,针对 ({{bar partial }_b}) -方程的解,Amar 的 Lp-estimations 和 Berndtsson 的 L2-estimations 起到了至关重要的作用。此外,我们还解决了有界强伪凸域的哈代空间 Hp(Ω) (1 ≤ p ≤ ∞) 的格里森问题。
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引用次数: 0
The global existence of strong solutions for a non-isothermal ideal gas system 非等温理想气体系统强解的全局存在性
IF 1 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-01 DOI: 10.1007/s10473-024-0306-9

Abstract

We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach. We first show the global well-posedness in the Sobolev space H2 (ℝ3) for solutions near equilibrium through iterated energy-type bounds and a continuity argument. We then prove the global well-posedness in the critical Besov space (dot{boldsymbol{B}}_{boldsymbol{2,1}}^{boldsymbol{3/2}}) by showing that the linearized operator is a contraction mapping under the right circumstances.

摘要 我们研究了从能量变分法导出的非等温理想气体模型强解的全局存在性。首先,我们通过迭代能量型约束和连续性论证,证明了在 Sobolev 空间 H2 (ℝ3) 中接近平衡解的全局好求解性。然后,我们通过证明线性化算子在适当情况下是一个收缩映射,证明了临界贝索夫空间 (dot{boldsymbol{B}}_{boldsymbol{2,1}}^{boldsymbol{3/2}})中的全局可求性。
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引用次数: 0
The boundary Schwarz lemma and the rigidity theorem on Reinhardt domains B p n of ℂn ℂn的莱因哈特域B p n上的边界施瓦茨定理和刚性定理
IF 1 4区 数学 Q1 MATHEMATICS Pub Date : 2024-05-01 DOI: 10.1007/s10473-024-0304-y

Abstract

By introducing the Carathéodory metric, we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B p n of ℂn. Furthermore, the boundary rigidity theorem for holomorphic self-mappings defined on B p n is obtained. These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for p = 2, and the unit polydisk for p = ∞, respectively.

摘要 通过引入 Carathéodory 度量,我们建立了ℂn 的单位 p 球 B p n 上全形自映射的边界施瓦茨 Lemma。此外,我们还得到了定义在 B p n 上的全形自映射的边界刚性定理。这些结果分别涵盖了 p = 2 时单位球上的全形自贴图的边界施瓦茨 Lewarz Lemma 和刚性结果,以及 p = ∞ 时单位多盘上的全形自贴图的边界刚性结果。
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引用次数: 0
Starlikeness associated with the sine hyperbolic function 与正弦双曲线函数相关的星光性
IF 1 4区 数学 Q1 MATHEMATICS Pub Date : 2024-04-16 DOI: 10.1007/s10473-024-0404-8
Mohsan Raza, Hadiqa Zahid, Jinlin Liu

Let (z) = 1 + λsinh(ς), 0 < λ < 1/sinh(1) be a non-vanishing analytic function in the open unit disk. We introduce a subclass ({{cal S}^ * }({q_lambda })) () of starlike functions which contains the functions (mathfrak{f}) such that (z{mathfrak{f}^prime }/mathfrak{f}) is subordinated by . We establish inclusion and radii results for the class ({{cal S}^ * }) () for several known classes of starlike functions. Furthermore, we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class ({{cal S}^ * }) (). We also find a sharp bound for the third Hankel determinant for the case λ = 1/2.

让 qλ (z) = 1 + λsinh(ς), 0 < λ < 1/sinh(1)是开放单位盘中的非消失解析函数。我们引入了星状函数的子类 ({{cal S}^ * }({q_lambda })) (qλ),它包含函数 (mathfrak{f}/),使得 (z{mathfrak{f}^prime }/mathfrak{f}) 从属于 qλ。我们为几类已知的星状函数建立了类 ({{cal S}^ * }) (qλ) 的包含和半径结果。此外,我们还得到了类({{cal S}^ * }) (qλ)的二阶尖锐系数边界和尖锐汉克尔行列式。在 λ = 1/2 的情况下,我们还找到了第三个汉克尔行列式的尖锐边界。
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引用次数: 0
Blow-up conditions for a semilinear parabolic system on locally finite graphs 局部有限图上半线性抛物系统的炸毁条件
IF 1 4区 数学 Q1 MATHEMATICS Pub Date : 2024-03-01 DOI: 10.1007/s10473-024-0213-0

Abstract

In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).

摘要 本文研究了局部有限图上半线性抛物系统的炸毁现象。在曲率条件 CDE'(n,0)、度数为 m 的多项式体积增长、初始值和吸收项指数的一些适当假设下,我们证明了半线性抛物线系统的每个非负解都会在有限时间内炸毁。我们目前的工作扩展了 Lin 和 Wu(Calc Var Partial Differ Equ,2017,56:Art 102)以及 Wu(Rev R Acad Cien Serie A Mat,2021,115:Art 133)取得的成果。
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引用次数: 0
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Acta Mathematica Scientia
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