SIAM Journal on Mathematical Analysis最新文献_第8页

The Anisotropic Calderón Problem for High Fixed Frequency 高固定频率的各向异性卡尔德龙问题

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-04 DOI: 10.1137/23m1579029

Gunther Uhlmann, Yiran Wang

引用次数: 0

Quasi-linear Fractional-Order Operators in Lipschitz Domains Lipschitz 域中的准线性分阶算子

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-04 DOI: 10.1137/23m1575871

Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto

引用次数: 0

Principal Spectral Theory of Time-Periodic Nonlocal Dispersal Cooperative Systems and Applications 时间周期性非局部分散合作系统的主频谱理论及其应用

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-04 DOI: 10.1137/22m1543902

Yan-Xia Feng, Wan-Tong Li, Shigui Ruan, Ming-Zhen Xin

引用次数: 0

Nonlocal Partial Differential Equations and Quantum Optics: Bound States and Resonances 非局部偏微分方程与量子光学：边界态和共振

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-03 DOI: 10.1137/23m158142x

Erik Orvehed Hiltunen, Joseph Kraisler, John C. Schotland, Michael I. Weinstein

{"title":"Nonlocal Partial Differential Equations and Quantum Optics: Bound States and Resonances","authors":"Erik Orvehed Hiltunen, Joseph Kraisler, John C. Schotland, Michael I. Weinstein","doi":"10.1137/23m158142x","DOIUrl":"https://doi.org/10.1137/23m158142x","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3802-3831, June 2024. <br/> Abstract. We consider the quantum optics of a single photon interacting with a system of two-level atoms. The wave properties of this interacting system are determined by the spectral properties of a matrix Hamiltonian, involving a nonlocal partial differential operator, acting on photonic and atomic degrees of freedom. We study the spectral problem via a reduction to a spectral problem for a scalar nonlocal operator, which depends nonlinearly on the spectral parameter. We investigate two classes of solutions: Bound states are solutions that decay at infinity, while resonance states have locally finite energy and satisfy a non–self-adjoint outgoing radiation condition at infinity. We have found necessary and sufficient conditions for the existence of bound states, along with an upper bound on the number of such states. We have also considered these problems for atomic models with small, high-contrast inclusions. In this setting, we have derived asymptotic formulas for the resonances. Our results are illustrated with numerical computations.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Multiple Normalized Solutions for First Order Hamiltonian Systems 一阶哈密顿系统的多重归一化解法

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-03 DOI: 10.1137/23m1584575

Yuxia Guo, Yuanyang Yu

引用次数: 0

Multibump Solutions for Critical Choquard Equation 临界乔卡方程的多凸点解决方案

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-03 DOI: 10.1137/23m1581820

Jiankang Xia, Xu Zhang

引用次数: 0

Equilibrium Configurations of a Symmetric Body Immersed in a Stationary Navier–Stokes Flow in a Planar Channel 浸没在平面通道静态纳维-斯托克斯流中的对称体的平衡配置

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-03 DOI: 10.1137/23m1568752

Elvise Berchio, Denis Bonheure, Giovanni P. Galdi, Filippo Gazzola, Simona Perotto

{"title":"Equilibrium Configurations of a Symmetric Body Immersed in a Stationary Navier–Stokes Flow in a Planar Channel","authors":"Elvise Berchio, Denis Bonheure, Giovanni P. Galdi, Filippo Gazzola, Simona Perotto","doi":"10.1137/23m1568752","DOIUrl":"https://doi.org/10.1137/23m1568752","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3759-3801, June 2024. <br/> Abstract. We study the equilibrium configurations for several fluid-structure interaction problems. The fluid is confined in a 2D unbounded channel that contains a body, free to move inside the channel with rigid motions (transversal translations and rotations). The motion of the fluid is generated by a Poiseuille inflow/outflow at infinity and governed by the stationary Navier–Stokes equations. For a model where the fluid is the air and the body represents the cross-section of a suspension bridge, therefore also subject to restoring elastic forces, we prove that for small inflows there exists a unique equilibrium position, while for large inflows we numerically show the appearance of additional equilibria. A similar uniqueness result is also obtained for a discretized 3D bridge, consisting in a finite number of cross-sections interacting with the adjacent ones. The very same model, but without restoring forces, is used to describe the mechanism of the Leonardo da Vinci ferry, which is able to cross a river without engines. We numerically determine the optimal orientation of the ferry that allows it to cross the river in minimal time.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

On the Boussinesq Hypothesis for a Stochastic Proudman–Taylor Model 论随机普鲁德曼-泰勒模型的布辛斯克假说

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-03 DOI: 10.1137/23m1587944

Franco Flandoli, Dejun Luo

引用次数: 0

On Scaling Properties for a Class of Two-Well Problems for Higher Order Homogeneous Linear Differential Operators 论高阶均质线性微分算子的一类两井问题的缩放特性

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-05-31 DOI: 10.1137/23m1588287

Bogdan Raiţă, Angkana Rüland, Camillo Tissot, Antonio Tribuzio

{"title":"On Scaling Properties for a Class of Two-Well Problems for Higher Order Homogeneous Linear Differential Operators","authors":"Bogdan Raiţă, Angkana Rüland, Camillo Tissot, Antonio Tribuzio","doi":"10.1137/23m1588287","DOIUrl":"https://doi.org/10.1137/23m1588287","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3720-3758, June 2024. <br/> Abstract. We study the scaling behavior of a class of compatible two-well problems for higher order, homogeneous linear differential operators. To this end, we first deduce general lower scaling bounds which are determined by the vanishing order of the symbol of the operator on the unit sphere in the direction of the associated element in the wave cone. We complement the lower bound estimates by a detailed analysis of the two-well problem for generalized (tensor-valued) symmetrized derivatives with the help of the (tensor-valued) Saint-Venant compatibility conditions. In two spatial dimensions for highly symmetric boundary data (but arbitrary tensor order [math]) we provide upper bound constructions matching the lower bound estimates. This illustrates that for the two-well problem for higher order operators new scaling laws emerge which are determined by the Fourier symbol in the direction of the wave cone. The scaling for the symmetrized gradient from [A. Chan and S. Conti, Math. Models Methods Appl. Sci., 25 (2015), pp. 1091–1124] which was also discussed in [B. Raiță, A. Rüland, and C. Tissot, Acta Appl. Math., 184 (2023), 5] provides an example of this family of new scaling laws.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Pinning in the Extended Lugiato–Lefever Equation 扩展卢吉亚托-勒弗弗方程中的针刺效应

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-05-31 DOI: 10.1137/23m1550700

Lukas Bengel, Dmitry Pelinovsky, Wolfgang Reichel

{"title":"Pinning in the Extended Lugiato–Lefever Equation","authors":"Lukas Bengel, Dmitry Pelinovsky, Wolfgang Reichel","doi":"10.1137/23m1550700","DOIUrl":"https://doi.org/10.1137/23m1550700","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3679-3702, June 2024. <br/> Abstract. We consider a variant of the Lugiato–Lefever equation (LLE), which is a nonlinear Schrödinger equation on a one-dimensional torus with forcing and damping, to which we add a first-order derivative term with a potential [math]. The potential breaks the translation invariance of LLE. Depending on the existence of zeroes of the effective potential [math], which is a suitably weighted and integrated version of [math], we show that stationary solutions from [math] can be continued locally into the range [math]. Moreover, the extremal points of the [math]-continued solutions are located near zeros of [math]. We therefore call this phenomenon pinning of stationary solutions. If we assume additionally that the starting stationary solution at [math] is spectrally stable with the simple zero eigenvalue due to translation invariance being the only eigenvalue on the imaginary axis, we can prove asymptotic stability or instability of its [math]-continuation depending on the sign of [math] at the zero of [math] and the sign of [math]. The variant of the LLE arises in the description of optical frequency combs in a Kerr nonlinear ring-shaped microresonator which is pumped by two different continuous monochromatic light sources of different frequencies and different powers. Our analytical findings are illustrated by numerical simulations.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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