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Polynomial perturbations of Euler's and Clausen's identities 欧拉恒等式和克劳森恒等式的多项式摄动

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2026-01-16 DOI: 10.1016/j.aam.2026.103042

Dmitrii Karp

A product of two hypergeometric series is generally not hypergeometric. However, there are a few cases when such a product does reduce to a single hypergeometric series. The oldest result of this type, beyond the obvious

{(1 - x)}^{a} {(1 - x)}^{b} = {(1 - x)}^{a + b}

, is Euler's transformation for the Gauss hypergeometric function

{}_{2}F_{1}

. Another important one is the celebrated Clausen's identity, dating back to 1828, which expresses the square of a suitable

{}_{2}F_{1}

function as a single

{}_{3}F_{2}

. By equating coefficients, each product identity corresponds to a special type of summation theorem for terminating series. Over the last two decades Euler's transformations and many summation theorems have been extended by introducing additional parameter pairs differing by positive integers. This amounts to multiplication of the power series coefficients by values of a fixed polynomial at nonnegative integers. The main goal of this paper is to present an extension of Clausen's identity obtained by such polynomial perturbation. To this end, we first reconsider the polynomial perturbations of Euler's transformations found by Miller and Paris around 2010. We propose new, simplified proofs of their transformations relating them to polynomial interpolation and exhibiting various new forms of the characteristic polynomials. We further introduce the notion of the Miller-Paris operators which play a prominent role in the construction of the extended Clausen's identity.

两个超几何级数的乘积一般不是超几何级数。然而，在少数情况下，这样的乘积确实简化为单个超几何级数。除了明显的（1−x）a(1−x)b=(1−x)a+b之外，这种类型最古老的结果是高斯超几何函数F12的欧拉变换。另一个重要的是著名的Clausen的身份，可以追溯到1828年，它将合适的F12函数的平方表示为单个F23。通过使系数相等，每个乘积恒等式对应于一种特殊类型的求和定理，用于终止级数。在过去的二十年里，欧拉变换和许多求和定理通过引入额外的参数对被正整数差分而得到了扩展。这相当于幂级数系数乘以非负整数上的固定多项式的值。本文的主要目的是给出由这种多项式摄动得到的克劳森恒等式的推广。为此，我们首先重新考虑Miller和Paris在2010年前后发现的欧拉变换的多项式摄动。我们提出了新的、简化的证明，证明了它们与多项式插值有关的变换，并展示了特征多项式的各种新形式。我们进一步介绍了米勒-巴黎算子的概念，它在扩展克劳森身份的构建中起着突出的作用。

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引用次数: 0

Extremal problems for multivalent functions 多价函数的极值问题

IF 0.7 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae

Pub Date : 2026-01-16 DOI: 10.1007/s00010-026-01264-y

Mamoru Nunokawa, Krzysztof Piejko, Janusz Sokół

In this paper we consider some sufficient conditions for a function to be at most p-valent in the unit disc on the complex plane which are related to the known Ozaki’s and Noshiro-Warschawski conditions.

本文在已知的Ozaki条件和Noshiro-Warschawski条件的基础上，研究了复平面上单位圆盘上函数最多为p价的几个充分条件。

引用次数: 0

Bohr type inequalities for certain integral operators and transforms on shifted disks 移位盘上某些积分算子和变换的玻尔型不等式

IF 1.6 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics

Pub Date : 2026-01-16 DOI: 10.1007/s13324-026-01163-0

Vasudevarao Allu, Raju Biswas, Rajib Mandal

In this paper, we derive the sharp Bohr type inequalities for the Cesáro operator, Bernardi integral operator, discrete Fourier transform and discrete Laplace transform acting on the class of bounded analytic functions defined on shifted disks

$$begin{aligned} Omega _{gamma }=left{ zin mathbb {C}:left| z+frac{gamma }{1-gamma }right| <frac{1}{1-gamma }right} quad text {for}quad gamma in [0,1).end{aligned}$$

本文导出了作用于移盘上有界解析函数的Cesáro算子、Bernardi积分算子、离散傅里叶变换和离散拉普拉斯变换的尖锐Bohr型不等式 $$begin{aligned} Omega _{gamma }=left{ zin mathbb {C}:left| z+frac{gamma }{1-gamma }right| <frac{1}{1-gamma }right} quad text {for}quad gamma in [0,1).end{aligned}$$

引用次数: 0

Fault tolerance for metric dimension and its variants 公制尺寸及其变体的容错

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-16 DOI: 10.1016/j.dam.2026.01.009

Jesse Geneson , Shen-Fu Tsai

<div><div>Hernando et al. (2008) introduced the fault-tolerant metric dimension <math><mrow><mtext>ftdim</mtext><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>, which is the size of the smallest resolving set <math><mi>S</mi></math> of a graph <math><mi>G</mi></math> such that <math><mrow><mi>S</mi><mo>−</mo><mfenced><mrow><mi>s</mi></mrow></mfenced></mrow></math> is also a resolving set of <math><mi>G</mi></math> for every <math><mrow><mi>s</mi><mo>∈</mo><mi>S</mi></mrow></math>. They found an upper bound <math><mrow><mtext>ftdim</mtext><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mo>dim</mo><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>2</mn><mi>⋅</mi><msup><mrow><mn>5</mn></mrow><mrow><mo>dim</mo><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math>, where <math><mrow><mo>dim</mo><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> denotes the standard metric dimension of <math><mi>G</mi></math>. It was unknown whether there exists a family of graphs where <math><mrow><mtext>ftdim</mtext><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> grows exponentially in terms of <math><mrow><mo>dim</mo><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>, until recently when Knor et al. (2024) found a family with <math><mrow><mtext>ftdim</mtext><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><mo>dim</mo><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>+</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>dim</mo><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> for any possible value of <math><mrow><mo>dim</mo><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>. We improve the upper bound on fault-tolerant metric dimension by showing that <math><mrow><mtext>ftdim</mtext><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mo>dim</mo><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mrow><mn>3</mn></mrow><mrow><mo>dim</mo><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math> for every connected graph <math><mi>G</mi></math>. Moreover, we find an infinite family of connected graphs <math><msub><mrow><mi>J</mi></mrow><mrow><mi>k</mi></mrow></msub></math> such that <math><mrow><mo>dim</mo><mrow><mo>(</mo><msub><mrow><mi>J</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mi>k</mi></mrow></math> and <math><mrow><mtext>ftdim</mtext><mrow><mo>(</mo><msub><mrow><mi>J</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow><mo>≥</mo><msup><mrow><mn>3</mn></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>−</mo><mi>k</mi><mo>−</mo><mn>1</mn></mrow></mat

Hernando et al.（2008）引入了容错度量维度ftdim(G)，它是图G的最小解析集S的大小，使得S−S也是每个S∈S的G的解析集。他们发现了一个上界ftdim(G)≤dim(G)(1+2·5dim(G)−1)，其中dim(G)表示G的标准度量维度。不知道是否存在一类图，其中ftdim(G)以dim(G)为指数增长，直到最近Knor等人（2024）发现ftdim(G)=dim(G)+2dim(G)−1对于任何可能的dim(G)值。通过证明对于每一个连通图G， ftdim(G)≤dim(G)(1+3dim(G)−1)，我们改进了容错度量维的上界，并且我们找到了一个无限族的连通图Jk，使得对于每一个正整数k， dim(Jk)=k和ftdim(Jk)≥3k−1−k−1。我们的结果表明limk→∞maxG:dim(G)=klog3(ftdim(G))k=1。此外，我们考虑容错边缘度量维数ftedim(G)，并将其与边缘度量维数edim(G)进行定界，表明limk→∞maxG:edim(G)=klog2(ftedim(G))k=1。我们还得到了邻接维数和k截断度量维数容错的尖锐极值界。此外，我们还得到了其他一些关于度量维数及其变体的极值问题的尖锐界。特别地，我们证明了关于边度量维的极值问题与极值集理论中Erdős和Kleitman（1974）的开放问题之间的等价性。

引用次数: 0

Half-space theorems for translating solitons of the r-mean curvature flow r-平均曲率流的平移孤子的半空间定理

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114115

Hilário Alencar , G. Pacelli Bessa , Gregório Silva Neto

In this paper, we establish nonexistence results for complete translating solitons of the r-mean curvature flow under suitable growth conditions on the

(r - 1)

-mean curvature and on the norm of the second fundamental form. We first show that such solitons cannot be entirely contained in the complement of a right rotational cone whose axis of symmetry is aligned with the translation direction. We then relax the growth condition on the

(r - 1)

-mean curvature and prove that properly immersed translating solitons cannot be confined to certain half-spaces opposite to the translation direction. We conclude the paper by showing that complete, properly immersed translating solitons satisfying appropriate growth conditions on the

(r - 1)

-mean curvature cannot lie completely within the intersection of two transversal vertical half-spaces.

本文在(r−1)-平均曲率和第二基本形式的范数上，建立了适当生长条件下r-平均曲率流的完全平移孤子的不存在性结果。我们首先证明了这样的孤子不能完全包含在对称轴与平移方向对齐的右旋转锥的补中。然后我们放宽了(r−1)-平均曲率上的生长条件，并证明了适当浸入的平移孤子不能局限于与平移方向相反的某些半空间。我们通过证明在(r−1)-平均曲率上满足适当生长条件的完全的、适当浸入的平移孤子不能完全位于两个横向垂直半空间的交点内来结束本文。

引用次数: 0

On DP-coloring of outerplanar graphs 关于外平面图的dp染色

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-16 DOI: 10.1016/j.disc.2026.114996

Tianjiao Dai , Jie Hu , Hao Li , Shun-ichi Maezawa

The notion of DP-coloring was introduced by Dvořák and Postle which is a generalization of list coloring. A DP-coloring of a graph G reduces the problem of finding a proper coloring of G from a given list L to the problem of finding a “large” independent set in an auxiliary graph

M_{L}

-cover with a vertex set

{(v, c) : v \in V (G)

and

c \in L (v)}

. Hutchinson (Journal of Graph Theory, 2008) showed that

•
if a 2-connected bipartite outerplanar graph G has a list of colors $L (v)$ for each vertex v with $| L (v) | \geq \min {\deg_{G} (v), 4}$ , then G is L-colorable; and
•
if a 2-connected maximal outerplanar graph G with at least four vertices has a list of colors $L (v)$ for each vertex v with $| L (v) | \geq \min {\deg_{G} (v), 5}$ , then G is L-colorable.

In this paper, we study whether bounds of Hutchinson's results hold for DP-coloring. We obtain that the first one is not sufficient for DP-coloring while the second one is sufficient.

dp -着色的概念是由Dvořák和Postle提出的，它是列表着色的推广。图G的dp -着色将从给定列表L中寻找G的适当着色问题简化为在具有顶点集{(v,c):v∈v (G) and c∈L(v)}的辅助图ML-cover中寻找“大”独立集的问题。Hutchinson （Journal of Graph Theory, 2008）证明了•如果一个2连通二部外平面图G对于每个顶点v有一个颜色列表L(v)且|L(v)|≥min (degG) {degG (v),4}，则G是L可色的；•如果一个至少有四个顶点的2连通最大外平面图G对每个顶点v都有一个颜色列表L(v)，且|L(v)|≥min (degG) (v),5}，则G是L可色的。在本文中，我们研究了Hutchinson结果的界对于dp -着色是否成立。我们得到第一个是不充分的，而第二个是充分的。

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引用次数: 0

Internal and boundary control-based fixed-time synchronization for stochastic impulsive reaction-diffusion complex networks 基于内部和边界控制的随机脉冲反应扩散复杂网络固定时间同步

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2026-01-16 DOI: 10.1016/j.chaos.2026.117910

Ying Qiao , Rukeya Tohti , Binglong Lu , Abdujelil Abdurahman , Haijun Jiang

This paper focuses on the fixed-time (FXT) synchronization in probability of stochastic impulsive reaction–diffusion complex networks (SIRDCNs) with Robin boundary conditions (RBCs). Firstly, stochastic disturbances and impulsive effects are incorporated into the reaction–diffusion complex networks (RDCNs) to increase the generalization in practical applications. Then, the RBC that generates the Neumann and Dirichlet boundary conditions is employed, which offers greater flexibility than a single-type boundary condition. Subsequently, to achieve FXT synchronization in probability for the addressed SIRDCNs, this paper designs internal and boundary controllers, where the internal controller is implemented over the entire spatial domain, while the boundary controller only needs to be activated at the domain edges, thereby it is more economic and fits well the real application scenarios. Furthermore, some novel criteria for FXT synchronization in probability of considered network are derived through the Lyapunov functional method and stochastic analysis. Finally, numerical simulations are performed to verify the validity of the proposed criteria.

研究了具有Robin边界条件的随机脉冲反应扩散复杂网络（SIRDCNs）的概率定时同步问题。首先，在反应扩散复杂网络（RDCNs）中加入随机干扰和脉冲效应，提高其在实际应用中的泛化能力。然后，采用生成诺伊曼和狄利克雷边界条件的RBC，这比单一类型的边界条件提供了更大的灵活性。随后，为了实现寻址SIRDCNs的概率FXT同步，本文设计了内部控制器和边界控制器，其中内部控制器在整个空间域中实现，而边界控制器只需要在域边缘激活，因此更经济，更符合实际应用场景。在此基础上，利用李雅普诺夫泛函方法和随机分析方法，推导出了考虑网络FXT同步概率的一些新的判据。最后，通过数值仿真验证了所提准则的有效性。

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引用次数: 0

Smoothing property assumptions for uniformly differential processes acting on time-dependent normed spaces 作用于时相关赋范空间的一致微分过程的平滑性假设

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114103

Tomás Caraballo , Alexandre N. Carvalho , Arthur C. Cunha , Heraclio López-Lázaro

In this paper, we introduce the concept of uniformly differentiable evolution processes for dynamical systems on families of time-dependent phase spaces. This framework is motivated by two main aspects: it provides an appropriate framework for studying the dynamics of solutions to non-cylindrical PDE problems, and it naturally extends the theory of uniformly differentiable evolution processes on fixed phase spaces. We establish sufficient conditions on the differential of the evolution process, decomposed as the sum of a contraction and an operator with compactness properties, ensuring that the associated pullback attractors have finite fractal dimension. Our approach is inspired by the smoothing property, Mañé's method, and techniques for controlling backward bounded trajectories. As an application, we analyze non-cylindrical problems with different geometries, studying the dynamics of solutions for the one-dimensional semilinear heat equation and for the two-dimensional Navier-Stokes equations.

本文引入了时变相空间族上动力系统一致可微演化过程的概念。该框架的动机主要有两个方面：它为研究非圆柱形PDE问题解的动力学提供了一个合适的框架，并且自然地扩展了固定相空间上一致可微演化过程的理论。我们建立了演化过程的微分的充分条件，将其分解为具有紧性的收缩算子和算子，从而保证了相关的回拉吸引子具有有限的分形维数。我们的方法受到平滑特性、Mañé的方法和控制后向有界轨迹的技术的启发。作为应用，我们分析了不同几何形状的非圆柱形问题，研究了一维半线性热方程和二维Navier-Stokes方程解的动力学。

引用次数: 0

Perfect proper edge colorings of regular bipartite graphs with rainbow C4-s 具有彩虹C4-s的正则二部图的完备真边着色

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-16 DOI: 10.1016/j.disc.2026.115005

András Gyárfás , Gábor N. Sárközy , Adam Zsolt Wagner

<div><div>We call a proper edge coloring of a bipartite graph <math><mi>G</mi><mo>=</mo><mo>[</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>]</mo></math> with <math><mo>|</mo><mi>X</mi><mo>|</mo><mo>=</mo><mo>|</mo><mi>Y</mi><mo>|</mo><mo>=</mo><mi>n</mi></math> a B-coloring if every 4-cycle of G is colored with four different colors. Denote by <math><msub><mrow><mi>q</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math> the smallest number of colors needed for a B-coloring of graph G. The question whether <math><msub><mrow><mi>q</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>n</mi></math> implies <math><mo>|</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>=</mo><mi>o</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> is from Burr, Erdős, Graham and Sós. A positive answer to this question would imply a positive answer to the famous <math><mo>(</mo><mn>7</mn><mo>,</mo><mn>4</mn><mo>)</mo></math>-conjecture of Brown, Erdős and Sós. Here we look at an interesting test case of this question. We call a B-coloring of a d-regular bipartite graph <math><mi>G</mi><mo>=</mo><mo>[</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>]</mo></math> with <math><mo>|</mo><mi>X</mi><mo>|</mo><mo>=</mo><mo>|</mo><mi>Y</mi><mo>|</mo><mo>=</mo><mi>n</mi></math> perfect if each color class forms a perfect matching in G (i.e. has n edges).</div><div>Let <math><mi>f</mi><mo>(</mo><mi>d</mi><mo>)</mo></math> be the minimal n such that there exists a perfect B-coloring of some d-regular bipartite graph <math><mi>G</mi><mo>=</mo><mo>[</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>]</mo></math> with <math><mo>|</mo><mi>X</mi><mo>|</mo><mo>=</mo><mo>|</mo><mi>Y</mi><mo>|</mo><mo>=</mo><mi>n</mi></math>. A test case of the question above is whether <math><mi>f</mi><mo>(</mo><mi>d</mi><mo>)</mo></math> is super-linear. We prove the affirmative answer for shifted colorings: defined by the matchings <math><msub><mrow><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msub></math><math><msub><mrow><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mrow><mo>{</mo><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>k</mi><mo>+</mo><mi>i</mi></mrow></msub><mo>)</mo><mspace></mspace><mo>|</mo><mspace></mspace><mn>0</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>i</mi><mo>∈</mo><mi>D</mi><mo>}</mo></mrow><mo>,</mo></math> where <math><mi>D</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>i</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>i</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>}</mo><

对于具有|X|=|Y|=n的二部图G=[X,Y]，如果G的每4个循环都有4种不同的颜色，我们称其为b -染色。用qB(G)表示图G的b -着色所需的最小颜色数。qB(G)=n是否意味着|E(G)|=o（n2）的问题来自Burr， Erdős， Graham和Sós。对这个问题的肯定回答意味着对Brown， Erdős和Sós著名的（7,4）猜想的肯定回答。下面我们来看这个问题的一个有趣的测试案例。我们称d正则二部图G=[X，Y]且|X|=|Y|=n的b -着色，如果每个颜色类在G中形成一个完美匹配（即有n条边）。设f(d)为最小n，使得某d正则二部图G=[X，Y]具有|X|=|Y|=n的完美b -着色。上述问题的一个测试用例是f(d)是否超线性。我们证明了移位着色的肯定答案：由MiMi={(xk,yk+i)|0≤k≤n−1，i∈D}定义，其中D={i1，…，id}∧[0,n−1]，k+i是模n计算的。利用szemer的诱导匹配引证，我们将这个结果推广到更一般的着色类，我们称之为平移不变着色。一般地，我们证明了对于奇数d 2d+1≤f(d)，对于偶d 2d - 1≤f(d)，并且等式只对某些对称设计的关联图成立。从Behrend构造我们得到f(d)≤declog (d)我们利用小双翼和对称设计的性质证明了f(3)=7,f(4)=8,f(5)=12,12≤f(6)≤14,f(7)=16。

引用次数: 0

Global well-posedness and large-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction 具有双曲热传导的可压缩Navier-Stokes方程的全局适定性和大时性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114111

Fucai Li , Houzhi Tang , Shuxing Zhang

The classical Fourier's law, which states that the heat flux is proportional to the temperature gradient, induces the paradox of infinite propagation speed for heat conduction. To accurately simulate the real physical process, the hyperbolic model of heat conduction named Cattaneo's law was proposed, which leads to the finite speed of heat propagation. A natural question is whether the large-time behavior of the heat flux for compressible flow would be different for these two laws. In this paper, we aim to address this question by studying the global well-posedness and the optimal time-decay rates of classical solutions to the compressible Navier-Stokes system with Cattaneo's law. By designing a new method, we obtain the optimal time-decay rates for the highest order derivatives of the heat flux, which cannot be derived for the system with Fourier's law by Matsumura and Nishida (1979) [25]. In this sense, our results first reveal the essential differences between the two laws.

经典的傅立叶定律指出热流密度与温度梯度成正比，这导致了热传导的无限传播速度悖论。为了准确地模拟真实的物理过程，提出了热传导的双曲模型，即Cattaneo定律，该定律导致热传播速度有限。一个自然的问题是，对于这两个定律，可压缩流的热通量的大时间行为是否会有所不同。本文通过研究具有Cattaneo定律的可压缩Navier-Stokes系统经典解的全局适定性和最优时间衰减率来解决这一问题。通过设计一种新的方法，我们得到了Matsumura和Nishida(1979)[25]用傅立叶定律无法得到的系统最高阶导数的最优时间衰减率。从这个意义上说，我们的结果首先揭示了两个定律之间的本质区别。

引用次数: 0

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