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Quarterly of Applied Mathematics最新文献

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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
Quarterly of Applied Mathematics Pub Date : 2022-06-29 DOI: 10.1090/qam/1637
Corentin Kilque
{"title":"Transverse instability of high frequency weakly stable quasilinear boundary value problems","authors":"Corentin Kilque","doi":"10.1090/qam/1637","DOIUrl":"https://doi.org/10.1090/qam/1637","url":null,"abstract":"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.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44908045","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}
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
Quarterly of Applied Mathematics Pub Date : 2022-05-26 DOI: 10.1090/qam/1625
R. Barthwal, T. Raja Sekhar
{"title":"Two-dimensional non-self-similar Riemann solutions for a thin film model of a perfectly soluble anti-surfactant solution","authors":"R. Barthwal, T. Raja Sekhar","doi":"10.1090/qam/1625","DOIUrl":"https://doi.org/10.1090/qam/1625","url":null,"abstract":"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 \u0000\u0000 \u0000 \u0000 x\u0000 −\u0000 y\u0000 \u0000 x-y\u0000 \u0000\u0000 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.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48021412","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}
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
Quarterly of Applied Mathematics Pub Date : 2022-05-16 DOI: 10.1090/qam/1624
Do Lan, P. Tuan
{"title":"On stability for semilinear generalized Rayleigh-Stokes equation involving delays","authors":"Do Lan, P. Tuan","doi":"10.1090/qam/1624","DOIUrl":"https://doi.org/10.1090/qam/1624","url":null,"abstract":"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.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42594948","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}
引用次数: 1
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
Quarterly of Applied Mathematics Pub Date : 2022-05-10 DOI: 10.1090/qam/1623
Seung‐Yeal Ha, Gyuyoung Hwang, Dohyun Kim
{"title":"Two-point correlation function and its applications to the Schrödinger-Lohe type models","authors":"Seung‐Yeal Ha, Gyuyoung Hwang, Dohyun Kim","doi":"10.1090/qam/1623","DOIUrl":"https://doi.org/10.1090/qam/1623","url":null,"abstract":"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-\u0000\u0000 \u0000 h\u0000 h\u0000 \u0000\u0000 Strichartz estimate and the uniform-stability of the SL models with respect to initial data.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41582760","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}
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
Quarterly of Applied Mathematics Pub Date : 2022-04-02 DOI: 10.1090/qam/1622
Vishnu Raveendran, E. Cirillo, A. Muntean
{"title":"Upscaling of a reaction-diffusion-convection problem with exploding non-linear drift","authors":"Vishnu Raveendran, E. Cirillo, A. Muntean","doi":"10.1090/qam/1622","DOIUrl":"https://doi.org/10.1090/qam/1622","url":null,"abstract":"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.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43745816","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}
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
Quarterly of Applied Mathematics Pub Date : 2022-03-30 DOI: 10.1090/qam/1619
J. Fabricius, Salvador Manjate, P. Wall
{"title":"Error estimates for pressure-driven Hele-Shaw flow","authors":"J. Fabricius, Salvador Manjate, P. Wall","doi":"10.1090/qam/1619","DOIUrl":"https://doi.org/10.1090/qam/1619","url":null,"abstract":"","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41618691","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}
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
Quarterly of Applied Mathematics Pub Date : 2022-03-22 DOI: 10.1090/qam/1611
I. Sigal
{"title":"Differential equations of quantum mechanics","authors":"I. Sigal","doi":"10.1090/qam/1611","DOIUrl":"https://doi.org/10.1090/qam/1611","url":null,"abstract":"We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48567205","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}
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
Quarterly of Applied Mathematics Pub Date : 2022-03-21 DOI: 10.1090/qam/1617
A. Laiadi
{"title":"The influence of surface tension and gravity on cavitating flow past an inclined plate in a channel","authors":"A. Laiadi","doi":"10.1090/qam/1617","DOIUrl":"https://doi.org/10.1090/qam/1617","url":null,"abstract":"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 \u0000\u0000 \u0000 γ\u0000 gamma\u0000 \u0000\u0000 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.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47592856","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}
引用次数: 0
The mean-field limit of the Cucker-Smale model on complete Riemannian manifolds 完全黎曼流形上Cucker-Smale模型的平均场极限
IF 0.8 4区 数学
Quarterly of Applied Mathematics Pub Date : 2022-03-21 DOI: 10.1090/qam/1613
Hyunjin Ahn, Seung‐Yeal Ha, Doheon Kim, F. Schlöder, Woojoo Shim
{"title":"The mean-field limit of the Cucker-Smale model on complete Riemannian manifolds","authors":"Hyunjin Ahn, Seung‐Yeal Ha, Doheon Kim, F. Schlöder, Woojoo Shim","doi":"10.1090/qam/1613","DOIUrl":"https://doi.org/10.1090/qam/1613","url":null,"abstract":"We study the mean-field limit of the Cucker-Smale (C-S) model for flocking on complete smooth Riemannian manifolds. For this, we first formally derive the kinetic manifold C-S model on manifolds using the BBGKY hierarchy and derive several a priori estimates on emergent dynamics. Then, we present a rigorous mean-field limit from the particle model to the corresponding kinetic model by using the generalized particle-in-cell method. As a byproduct of our rigorous mean-field limit estimate, we also establish a global existence of a measure-valued solution for the derived kinetic model. Compared to the corresponding results on \u0000\u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 d\u0000 \u0000 mathbb {R}^d\u0000 \u0000\u0000, our procedure requires additional assumption on holonomy and proper a priori bound on the derivative of parallel transports. As a concrete example, we verify that hyperbolic space \u0000\u0000 \u0000 \u0000 \u0000 H\u0000 \u0000 d\u0000 \u0000 mathbb {H}^d\u0000 \u0000\u0000 satisfies our proposed standing assumptions.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45905864","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}
引用次数: 7
Time-asymptotic stability for first-order symmetric hyperbolic systems of balance laws in dissipative compressible fluid dynamics 耗散可压缩流体动力学中一阶对称双曲平衡律系统的时间渐近稳定性
IF 0.8 4区 数学
Quarterly of Applied Mathematics Pub Date : 2022-03-15 DOI: 10.1090/qam/1620
H. Freistühler
{"title":"Time-asymptotic stability for first-order symmetric hyperbolic systems of balance laws in dissipative compressible fluid dynamics","authors":"H. Freistühler","doi":"10.1090/qam/1620","DOIUrl":"https://doi.org/10.1090/qam/1620","url":null,"abstract":"This paper identifies a non-(or /iso-)thermal variant of Ruggeri’s 1983 formulation of viscous heat-conductive fluid dynamics as a hyperbolic system of balance laws and shows that both the original model and this variant have (a) time-asymptotically stable equilibria and (b) principal parts deriving from a protopotential: a single scalar function that induces the temporospatial flux as an appropriate part of its Hessian.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45557377","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}
引用次数: 3
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