Ricerche di Matematica最新文献

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Energy decay of wave equations with infinite memory effects versus supercritical frictional dampings 具有无限记忆效应与超临界摩擦阻尼的波方程能量衰减

IF 1.2 4区数学 Q1 MATHEMATICS

Ricerche di Matematica

Pub Date : 2023-12-11 DOI: 10.1007/s11587-023-00832-7

Menglan Liao

In this paper, a class of damped viscoelastic wave equations

$$begin{aligned} u_{tt}-k(0)Delta u-int _0^infty k'(s)Delta u(t-s)ds+|u_t|^{m-1}u_t=|u|^{p-1}u end{aligned}$$

is considered in a bounded domain (Omega subset {mathbb {R}}^3). Uniform energy decay was discussed which depends on the relaxation function (-k'(s)) in the previous work (Guo et al., Z Angew Math Phys 69:65, 2018) for (1le mle 5). Depending on a key integral inequality obtained by Martinez (ESAIM Control Optim Calc Var 4:419–444, 1999), we establish the decay estimate of the total energy for (m>5). Our results improve and complement the previous one. As an example, a logarithmic energy decay is also presented.

本文考虑了有界域 (Omega subset {mathbb {R}}^3) 中的一类阻尼粘弹性波方程 $$begin{aligned}u_{tt}-k(0)Delta u-int _0^infty k'(s)Delta u(t-s)ds+|u_t|^{m-1}u_t=|u|^{p-1}u end{aligned}$$。在之前的工作（Guo et al., Z Angew Math Phys 69:65, 2018）中，针对(1le mle 5)讨论了取决于弛豫函数(-k'(s))的均匀能量衰减。根据马丁内斯（ESAIM Control Optim Calc Var 4:419-444，1999）获得的关键积分不等式，我们建立了对（m>5 ）总能量的衰变估计。我们的结果改进并补充了之前的结果。作为一个例子，我们还提出了对数能量衰减。

引用次数: 0

A hyperbolic reaction–diffusion model of chronic wasting disease 慢性消耗性疾病的双曲线反应-扩散模型

IF 1.2 4区数学 Q1 MATHEMATICS

Ricerche di Matematica

Pub Date : 2023-12-09 DOI: 10.1007/s11587-023-00831-8

Elvira Barbera, Annamaria Pollino

A hyperbolic reaction–diffusion model is developed in the framework of Extended Thermodynamics in order to describe the spatio-temporal dynamics of populations afflicted by chronic wasting diseases. The hyperbolic structure of the system guarantees that the wave processes occur at finite velocity, so that the paradox of instantaneous diffusion, typical of parabolic systems, is removed. The character of steady states, together with the Hopf bifurcation, are investigated through linear stability analysis. The model is integrated numerically to valuate the behavior of the populations. Finally, the propagation of acceleration waves is analyzed.

本文在扩展热力学的框架内建立了一个双曲线反应-扩散模型，以描述慢性消耗性疾病患者的时空动态。该系统的双曲结构保证了波过程以有限速度发生，从而消除了抛物线系统中典型的瞬时扩散悖论。通过线性稳定性分析，研究了稳定状态的特征以及霍普夫分岔。对模型进行数值积分，以评估种群的行为。最后，分析了加速波的传播。

引用次数: 0

Nilpotent groups whose difference graphs have positive genus 差分图有正格的幂零群

IF 1.2 4区数学 Q1 MATHEMATICS

Ricerche di Matematica

Pub Date : 2023-12-02 DOI: 10.1007/s11587-023-00830-9

Parveen, Jitender Kumar

The power graph of a finite group G is a simple undirected graph with vertex set G and two vertices are adjacent if one is a power of the other. The enhanced power graph of a finite group G is a simple undirected graph whose vertex set is the group G and two vertices a, b are adjacent if there exists (c in G) such that both a and b are powers of c. In this paper, we study the difference graph (mathcal {D}(G)) of a finite group G which is the difference of the enhanced power graph and the power graph of G with all isolated vertices removed. We characterize all the finite nilpotent groups G such that the genus (or cross-cap) of the difference graph (mathcal {D}(G)) is at most 2.

有限群G的幂图是一个简单的无向图，其顶点集G和两个顶点相邻，如果其中一个是另一个的幂。有限群G的增强幂图是一个简单无向图，其顶点集为群G，且两个顶点a, b相邻，如果存在(c in G)使得a和b都是c的幂。本文研究了有限群G的差分图(mathcal {D}(G))，该差分图是所有孤立顶点被去掉后增强幂图与G的幂图之差。我们刻画了所有有限幂零群G，使得差分图(mathcal {D}(G))的属(或交叉帽)不超过2。

引用次数: 0

Some notes on the algebraic structure of linear recurrent sequences 关于线性循环序列代数结构的一些注意事项

IF 1.2 4区数学 Q1 MATHEMATICS

Ricerche di Matematica

Pub Date : 2023-11-27 DOI: 10.1007/s11587-023-00826-5

Gessica Alecci, Stefano Barbero, Nadir Murru

Several operations can be defined on the set of all linear recurrent sequences, such as the binomial convolution (Hurwitz product) or the multinomial convolution (Newton product). Using elementary techniques, we prove that this set equipped with the termwise sum and the aforementioned products is an R-algebra, given any commutative ring R with identity. Moreover, we provide explicitly a characteristic polynomial of the Hurwitz product and Newton product of any two linear recurrent sequences. Finally, we also investigate whether these R-algebras are isomorphic, considering also the R-algebras obtained using the Hadamard product and the convolution product.

在所有线性循环序列的集合上可以定义一些运算，如二项式卷积(Hurwitz积)或多项卷积(Newton积)。利用初等技术，证明了给定任意具有单位元的交换环R，这个具有项和和积的集合是一个R代数。并给出了任意两个线性循环序列的Hurwitz积和Newton积的特征多项式。最后，我们还研究了这些r -代数是否同构，同时考虑了用Hadamard积和卷积积得到的r -代数。

引用次数: 0

Existence of solutions for the problem of microwave heating and a Liapunoff criteria for stability and instability 微波加热问题解的存在性及稳定性和不稳定性的Liapunoff判据

IF 1.2 4区数学 Q1 MATHEMATICS

Ricerche di Matematica

Pub Date : 2023-11-26 DOI: 10.1007/s11587-023-00825-6

Giovanni Cimatti

The Galerkin’s method is applied to prove the existence of at least one solution of the initial boundary value problem for the nonlinear system of partial differential equations modelling the electromagnetic heating of materials. In addition a criteria of stability and instability based on a Liapunoff function is presented.

应用伽辽金方法证明了材料电磁加热非线性偏微分方程组初边值问题至少有一个解的存在性。此外，还提出了基于李雅普诺夫函数的稳定性和不稳定性判据。

引用次数: 0

On the dynamics of a Leslie–Gower predator–prey ternary model with intraguild 带内野的Leslie-Gower捕食-食饵三元模型动力学研究

4区数学 Q1 MATHEMATICS

Ricerche di Matematica

Pub Date : 2023-11-04 DOI: 10.1007/s11587-023-00822-9

C. Accarino, F. Capone, R. De Luca, G. Massa

Abstract In this paper, a predator–prey model with intraguild predation describing the evolution between three interacting species—namely prey, mesopredator and top predator—is investigated, with the aim to model a complete food web. In particular, the longtime behaviour of the solutions is analysed, proving the existence of an absorbing set, and the linear and nonlinear stability analyses of the coexistence equilibrium are performed.

摘要本文研究了一个捕食者-食饵模型，该模型描述了捕食者、中捕食者和顶级捕食者这三个相互作用的物种之间的进化过程，旨在建立一个完整的食物网模型。特别地，分析了解的长期行为，证明了吸收集的存在性，并进行了共存平衡的线性和非线性稳定性分析。

引用次数: 0

Hopf bifurcation and Turing patterns for a diffusive predator–prey system with weak Allee effect 具有弱Allee效应的扩散捕食系统的Hopf分岔和图灵模式

4区数学 Q1 MATHEMATICS

Ricerche di Matematica

Pub Date : 2023-11-03 DOI: 10.1007/s11587-023-00824-7

Wenbin Yang, Xin Chang

引用次数: 0

Group identities on symmetric units under oriented involutions in group algebras 群代数中有向对合下对称单位上的群恒等式

4区数学 Q1 MATHEMATICS

Ricerche di Matematica

Pub Date : 2023-10-25 DOI: 10.1007/s11587-023-00809-6

Alexander Holguín-Villa, John H. Castillo

Abstract Let $$mathbb {F}G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> denote the group algebra of a locally finite group G over the infinite field $$mathbb {F}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> </mml:math> with $$mathop {textrm{char}}nolimits (mathbb {F})ne 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>char</mml:mtext> <mml:mo>(</mml:mo> <mml:mi>F</mml:mi> <mml:mo>)</mml:mo> <mml:mo>≠</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , and let $$circledast :mathbb {F}Grightarrow mathbb {F}G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>⊛</mml:mo> <mml:mo>:</mml:mo> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> <mml:mo>→</mml:mo> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> denote the involution defined by $$alpha =Sigma alpha _{g}g mapsto alpha ^circledast =Sigma alpha _{g}sigma (g)g^{*}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mi>Σ</mml:mi> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mi>g</mml:mi> <mml:mo>↦</mml:mo> <mml:msup> <mml:mi>α</mml:mi> <mml:mo>⊛</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>Σ</mml:mi> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:msup> <mml:mi>g</mml:mi> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , where $$sigma :Grightarrow {pm 1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mo>:</mml:mo> <mml:mi>G</mml:mi> <mml:mo>→</mml:mo> <mml:mo>{</mml:mo> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> is a group homomorphism (called an orientation) and $$*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:math> is an involution of the group G . In this paper we prove, under some assumptions, that if the $$circledast $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>⊛</mml:mo> </mml:math> -symmetric units of $$mathbb {F}G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> satisfies a group identity then $$mathbb {F}G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> satisfies a polynomial identity, i.e., we give an affirmative answer to a Conjecture of B. Hartley in this setting. Moreover, in the case when the prime radical $$eta (mathbb {F}G)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>η</mml:mi> <mml:mo>(</mml:mo> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:m

抽象Let $$mathbb {F}G$$ fg表示无限域上的局部有限群G的群代数 $$mathbb {F}$$ F with $$mathop {textrm{char}}nolimits (mathbb {F})ne 2$$ char (F)≠2，让 $$circledast :mathbb {F}Grightarrow mathbb {F}G$$ : F G→F G表示由 $$alpha =Sigma alpha _{g}g mapsto alpha ^circledast =Sigma alpha _{g}sigma (g)g^{*}$$ α = Σ α g g∑α ＿ (l) = Σ α g Σ (g) g∗，其中 $$sigma :Grightarrow {pm 1}$$ σ: g→ { ±1 } 群同态(称为取向)和 $$*$$ *是G群的对合。在某些假设下，我们证明了 $$circledast $$ 的对称单位 $$mathbb {F}G$$ F G满足群恒等式 $$mathbb {F}G$$ F G满足一个多项式恒等式，即在这种情况下，我们对B. Hartley的一个猜想给出一个肯定的答案。而且，当质根 $$eta (mathbb {F}G)$$ 的η (F G) $$mathbb {F}G$$ 如果G是幂零的，我们描述了对称单位所对应的群 $$mathcal {U}^+(mathbb {F}G)$$ U + (F G)满足群恒等式。

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引用次数: 0

Turing instability for a Leslie–Gower model 莱斯利-高尔模型的图灵不稳定性

4区数学 Q1 MATHEMATICS

Ricerche di Matematica

Pub Date : 2023-10-11 DOI: 10.1007/s11587-023-00819-4

F. Capone, R. De Luca, L. Fiorentino, V. Luongo, G. Massa

Abstract The aim of this paper is to investigate a reaction-diffusion Leslie–Gower predator–prey model, incorporating the intraguild predation and both self and cross-diffusion. The longtime behaviour of the solutions is analysed, proving the existence of an absorbing set. The existence of patterns is investigated by looking for conditions guaranteeing that an equilibrium, stable in the absence of diffusion, becomes unstable when diffusion is allowed.

摘要本文研究了一个反应-扩散的Leslie-Gower捕食者-被食饵模型，该模型包含了种群内捕食、自扩散和交叉扩散。分析了解的长期行为，证明了吸收集的存在性。模式的存在性是通过寻找保证在没有扩散时稳定的平衡在允许扩散时变得不稳定的条件来研究的。

引用次数: 0

Correction: A chemotaxis reaction–diffusion model for Multiple Sclerosis with Allee effect 更正:具有Allee效应的多发性硬化症趋化反应-扩散模型

4区数学 Q1 MATHEMATICS

Ricerche di Matematica

Pub Date : 2023-10-10 DOI: 10.1007/s11587-023-00818-5

Marzia Bisi, Maria Groppi, Giorgio Martalò, Cinzia Soresina

引用次数: 0

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