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The Oberbeck–Boussinesq system with non-local boundary conditions 具有非局部边界条件的Oberbeck-Boussinesq系统

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics

Pub Date : 2022-06-30 DOI: 10.1090/qam/1635

A. Abbatiello, E. Feireisl

We consider the Oberbeck–Boussinesq system with non-local boundary conditions arising as a singular limit of the full Navier–Stokes–Fourier system in the regime of low Mach and low Froude numbers. The existence of strong solutions is shown on a maximal time interval [ 0 , T m a x ) [0, T_{mathrm {max}}) . Moreover, T m a x = ∞ T_{mathrm {max}} = infty in the two-dimensional setting.

我们认为，在低马赫数和低弗劳德数的情况下，具有非局部边界条件的Oberbeck–Boussinesq系统是全Navier–Stokes–Fourier系统的奇异极限。在极大时间区间[0，Tm a x）[0，T_｛mathrm｛max｝｝）上证明了强解的存在性}=infty在二维设置中。

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引用次数: 5

Transverse instability of high frequency weakly stable quasilinear boundary value problems 高频弱稳定拟线性边值问题的横向不稳定性

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics

Pub Date : 2022-06-29 DOI: 10.1090/qam/1637

Corentin Kilque

This work intends to prove that strong instabilities may appear for high order geometric optics expansions of weakly stable quasilinear hyperbolic boundary value problems, when the forcing boundary term is perturbed by a small amplitude oscillating function, with a transverse frequency. Since the boundary frequencies lie in the locus where the so-called Lopatinskii determinant is zero, the amplifications on the boundary give rise to a highly coupled system of equations for the profiles. A simplified model for this system is solved in an analytical framework using the Cauchy-Kovalevskaya theorem as well as a version of it ensuring analyticity in space and time for the solution. Then it is proven that, through resonances and amplification, a particular configuration for the phases may create an instability, in the sense that the small perturbation of the forcing term on the boundary interferes at the leading order in the asymptotic expansion of the solution. Finally we study the possibility for such a configuration of frequencies to happen for the isentropic Euler equations in space dimension three.

这项工作旨在证明，当强迫边界项受到具有横向频率的小振幅振荡函数的扰动时，弱稳定拟线性双曲边值问题的高阶几何光学展开可能出现强不稳定性。由于边界频率位于所谓的Lopatinskii行列式为零的轨迹上，边界上的放大产生了轮廓的高度耦合方程组。该系统的简化模型在分析框架中使用Cauchy-Kovalevskaya定理以及它的一个版本来求解，该版本确保了解在空间和时间上的可分析性。然后证明，通过共振和放大，相位的特定配置可能会产生不稳定性，因为边界上的强迫项的小扰动在解的渐近展开中以领先阶进行干扰。最后，我们研究了在三维空间中等熵欧拉方程发生这种频率配置的可能性。

引用次数: 0

Two-dimensional non-self-similar Riemann solutions for a thin film model of a perfectly soluble anti-surfactant solution 二维非自相似黎曼解的薄膜模型的完全可溶的抗表面活性剂溶液

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics

Pub Date : 2022-05-26 DOI: 10.1090/qam/1625

R. Barthwal, T. Raja Sekhar

In this article, we construct non-self-similar Riemann solutions for a two-dimensional quasilinear hyperbolic system of conservation laws which describes the fluid flow in a thin film for a perfectly soluble anti-surfactant solution. The initial Riemann data consists of two different constant states separated by a smooth curve in x − y x-y plane, so without using self-similarity transformation and dimension reduction, we establish solutions for five different cases. Further, we consider interaction of all possible nonlinear waves by taking initial discontinuity curve as a parabola to develop the structure of global entropy solutions explicitly.

在本文中，我们构造了二维拟线性双曲守恒律系统的非自相似Riemann解，该系统描述了完全可溶的反表面活性剂溶液在薄膜中的流体流动。初始黎曼数据由两个不同的常态组成，这两个常态在x−y x-y平面上由一条光滑曲线分隔，因此在不使用自相似变换和降维的情况下，我们建立了五种不同情况的解。此外，我们考虑了所有可能的非线性波的相互作用，将初始不连续曲线作为抛物线，明确地发展了全局熵解的结构。

引用次数: 2

On stability for semilinear generalized Rayleigh-Stokes equation involving delays 涉及时滞的半线性广义Rayleigh-Stokes方程的稳定性

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics

Pub Date : 2022-05-16 DOI: 10.1090/qam/1624

Do Lan, P. Tuan

We consider a functional semilinear Rayleigh-Stokes equation involving fractional derivative. Our aim is to analyze some circumstances, in those the global solvability, and asymptotic behavior of solutions are addressed. By establishing a Halanay type inequality, we show the dissipativity and asymptotic stability of solutions to our problem. In addition, we prove the existence of a compact set of decay solutions by using local estimates and fixed point arguments.

考虑一个包含分数阶导数的泛函半线性Rayleigh-Stokes方程。我们的目的是分析在某些情况下，解的全局可解性和渐近性。通过建立一个Halanay型不等式，证明了问题解的耗散性和渐近稳定性。此外，我们利用局部估计和不动点参数证明了一个紧集的衰减解的存在性。

引用次数: 1

A Diagnostic Insight of Dental Pulp Testing Methods in Pediatric Dentistry. 儿童牙科牙髓检测方法诊断透视》。

IF 2.4 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics

Pub Date : 2022-05-16 DOI: 10.3390/medicina58050665

Andreea Igna, Doina Mircioagă, Marius Boariu, Ștefan-Ioan Stratul

The accurate diagnosis of pulpal pathology in pediatric dentistry is essential for the success of vital pulp therapy. Pulp testing is often a challenging task due to understanding and cooperation issues of pediatric patients, as well as the particularities of pulpal physiology encountered in primary and immature permanent teeth. Sensibility tests, although still widely used by dental practitioners, are no longer recommended by pediatric specialists mainly due to their subjective nature. Vitality pulp tests have gained popularity in the last decade in light of some encouraging results of clinical studies. However, their use is not a routine practice yet. This paper is a literature review aimed to guide dental practitioners towards selecting the appropriate pulp testing method for their pediatric cases. It provides an overview on a multitude of pulp testing methods and an update in recommendations for primary and immature permanent teeth.

在儿童牙科中，准确诊断牙髓病变对成功进行重要的牙髓治疗至关重要。由于儿童患者的理解和合作问题，以及原牙和未成熟恒牙牙髓生理的特殊性，牙髓测试往往是一项具有挑战性的任务。虽然牙科医生仍在广泛使用感度测试，但由于其主观性，儿科专家已不再推荐使用。近十年来，由于临床研究取得了一些令人鼓舞的结果，牙髓活力测试逐渐受到欢迎。然而，这些测试尚未成为常规做法。本文是一篇文献综述，旨在指导牙科医生为儿科病例选择合适的牙髓测试方法。它概述了多种牙髓检测方法，并更新了针对乳恒牙和未成熟恒牙的建议。

引用次数: 0

Two-point correlation function and its applications to the Schrödinger-Lohe type models 两点相关函数及其在Schrödinger-Lohe型模型中的应用

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics

Pub Date : 2022-05-10 DOI: 10.1090/qam/1623

Seung‐Yeal Ha, Gyuyoung Hwang, Dohyun Kim

We study the asymptotic emergent dynamics and the continuum limit for the Schrödinger-Lohe (SL) model and semi-discrete SL model. For the SL model, emergent dynamics has been mostly studied for systems with identical potentials in literature. In this paper, we further extend emergent dynamics and stability estimate for the SL model with nonidentical potentials. To achieve this, we use two-point correlation functions defined as an inner product between wave functions. For the semi-discrete SL model, we provide a global unique solvability and a sufficient framework for the smooth transition from the semi-discrete SL model to the SL model in any finite-time interval, as the mesh size tends to zero. Our convergence estimate depends on the uniform-in- h h Strichartz estimate and the uniform-stability of the SL models with respect to initial data.

研究了Schrödinger-Lohe (SL)模型和半离散SL模型的渐近涌现动力学和连续极限。对于SL模型，文献中大多研究具有相同势的系统的涌现动力学。在本文中，我们进一步推广了具有非相同电位的SL模型的涌现动力学和稳定性估计。为了实现这一点，我们使用两点相关函数定义为波函数之间的内积。对于半离散SL模型，我们提供了一个全局唯一的可解性和一个充分的框架，使得半离散SL模型在任何有限时间间隔内，当网格大小趋于零时，可以平滑地从半离散SL模型过渡到SL模型。我们的收敛估计依赖于均匀- h - h strihartz估计和SL模型相对于初始数据的均匀稳定性。

引用次数: 2

Upscaling of a reaction-diffusion-convection problem with exploding non-linear drift 具有爆炸非线性漂移的反应-扩散-对流问题的放大

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics

Pub Date : 2022-04-02 DOI: 10.1090/qam/1622

Vishnu Raveendran, E. Cirillo, A. Muntean

We study a reaction-diffusion-convection problem with non-linear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. Because of the imposed large drift scaling, this non-linearity is expected to explode in the limit of a vanishing scaling parameter. As main working techniques, we employ two-scale formal homogenization asymptotics with drift to derive the corresponding upscaled model equations as well as the structure of the effective transport tensors. Finally, we use Schauder’s fixed point theorem as well as monotonicity arguments to study the weak solvability of the upscaled model posed in an unbounded domain. This study wants to contribute with theoretical understanding needed when designing thin composite materials that are resistant to high velocity impacts.

我们研究了具有非线性漂移的反应-扩散-对流问题，该问题是在具有周期性排列障碍物的区域中提出的。漂移中的非线性与完全不对称简单排除过程（TASEP）的流体动力学极限有关，该过程控制着穿过有障碍物的区域的相互作用粒子群。由于所施加的大漂移标度，预计这种非线性将在消失标度参数的极限下爆发。作为主要的工作技术，我们使用带漂移的两尺度形式化均匀化渐近性来导出相应的放大模型方程以及有效传输张量的结构。最后，我们使用Schauder不动点定理和单调性论点来研究在无界域中提出的放大模型的弱可解性。这项研究希望在设计耐高速冲击的薄复合材料时，有助于获得所需的理论理解。

引用次数: 2

Error estimates for pressure-driven Hele-Shaw flow 压力驱动Hele-Shaw流的误差估计

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics

Pub Date : 2022-03-30 DOI: 10.1090/qam/1619

J. Fabricius, Salvador Manjate, P. Wall

引用次数: 0

Differential equations of quantum mechanics 量子力学的微分方程

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics

Pub Date : 2022-03-22 DOI: 10.1090/qam/1611

I. Sigal

We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.

我们简要回顾了量子力学中涉及偏微分方程的一些重要领域的主要数学结构和结果，并提出了开放问题。

引用次数: 2

The influence of surface tension and gravity on cavitating flow past an inclined plate in a channel 表面张力和重力对槽内斜板空化流的影响

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics

Pub Date : 2022-03-21 DOI: 10.1090/qam/1617

A. Laiadi

This paper concerns the two-dimensional free surface cavity flow past an inclined plate in a finite depth. To close the cavity, a Riabouchinsky model is considered. The fluid is assumed to be inviscid and incompressible and the flow to be steady and irrotational. When the gravity and surface tension are negligible, an exact free streamline solution is derived. We solve the cavity flow problem by using two numerical methods. These methods allow us to compute solutions including the effects of gravity and surface tension. The first method is the series truncation and the second is the boundary integral equations, based on Cauchy integral formula. Numerical solutions are found for different values of the angle of inclination γ gamma and for various values of the Weber number, the Froude number. Good agreement between the two numerical schemes and the exact solution provides a check on the numerical methods.

本文研究了二维自由表面空腔在有限深度上通过斜板的流动问题。为了关闭空腔，考虑了Riabouchinsky模型。假定流体是无粘性和不可压缩的，流动是稳定和无旋转的。当重力和表面张力可以忽略不计时，得到了精确的自由流线解。本文采用两种数值方法求解空腔流动问题。这些方法使我们能够计算包括重力和表面张力影响的解。第一种方法是级数截断法，第二种方法是基于柯西积分公式的边界积分方程法。对于倾角γ γ的不同值和韦伯数、弗劳德数的不同值，找到了数值解。两种数值格式之间的良好一致性和精确解为数值方法提供了检验。

引用次数: 0

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