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Linearized Optimal Transport on Manifolds 曲面上的线性化最优传输
IF 2 2区 数学
SIAM Journal on Mathematical Analysis Pub Date : 2024-07-09 DOI: 10.1137/23m1564535
Clément Sarrazin, Bernhard Schmitzer
{"title":"Linearized Optimal Transport on Manifolds","authors":"Clément Sarrazin, Bernhard Schmitzer","doi":"10.1137/23m1564535","DOIUrl":"https://doi.org/10.1137/23m1564535","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4970-5016, August 2024. <br/> Abstract. Optimal transport is a geometrically intuitive, robust, and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This in turn leads to a reduction of computational complexity and simplifies combination with other methods that require a linear structure. Recently this approach has been extended to the unbalanced Hellinger–Kantorovich (HK) distance. In this article we further extend the framework in various ways, including measures on manifolds, the spherical HK distance, a study of the consistency of discretization via the barycentric projection, and the continuity properties of the logarithmic map for the HK distance.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"37 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572997","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
Gradient Regularity for a Class of Widely Degenerate Parabolic Systems 一类宽畸变抛物线系统的梯度正则性
IF 2 2区 数学
SIAM Journal on Mathematical Analysis Pub Date : 2024-07-09 DOI: 10.1137/23m1589232
Verena Bögelein, Frank Duzaar, Raffaella Giova, Antonia Passarelli di Napoli
{"title":"Gradient Regularity for a Class of Widely Degenerate Parabolic Systems","authors":"Verena Bögelein, Frank Duzaar, Raffaella Giova, Antonia Passarelli di Napoli","doi":"10.1137/23m1589232","DOIUrl":"https://doi.org/10.1137/23m1589232","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5017-5078, August 2024. <br/> Abstract. In this paper we study the [math] regularity of the weak solutions to the widely degenerate parabolic system [math] where [math], [math] is a parabolic cylinder with a bounded domain [math], and [math]. For the weak solutions [math] with [math], we prove that [math] is continuous in [math] for any continuous function [math] vanishing on the set [math].","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"20 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572996","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
Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Global Well-Posedness of Weakly Dissipative Systems 具有传输噪声和临界超线性扩散的反应-扩散方程：弱耗散系统的全局拟合
IF 2 2区 数学
SIAM Journal on Mathematical Analysis Pub Date : 2024-07-09 DOI: 10.1137/23m1562482
Antonio Agresti, Mark Veraar
{"title":"Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Global Well-Posedness of Weakly Dissipative Systems","authors":"Antonio Agresti, Mark Veraar","doi":"10.1137/23m1562482","DOIUrl":"https://doi.org/10.1137/23m1562482","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4870-4927, August 2024. <br/> Abstract. In this paper, we investigate the global well-posedness of reaction-diffusion systems with transport noise on the [math]-dimensional torus. We show new global well-posedness results for a large class of scalar equations (e.g., the Allen–Cahn equation) and dissipative systems (e.g., equations in coagulation dynamics). Moreover, we prove global well-posedness for two weakly dissipative systems: Lotka–Volterra equations for [math] and the Brusselator for [math]. Many of the results are also new without transport noise. The proofs are based on maximal regularity techniques, positivity results, and sharp blow-up criteria developed in our recent works, combined with energy estimates based on Itô’s formula and stochastic Gronwall inequalities. Key novelties include the introduction of new [math]-coercivity/dissipativity conditions and the development of an [math]-framework for systems of reaction-diffusion equations, which are needed when treating dimensions [math] in the case of cubic or higher order nonlinearities.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"19 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572999","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
Curvature Effects in Pattern Formation: Well-Posedness and Optimal Control of a Sixth-Order Cahn–Hilliard Equation 图案形成中的曲率效应：六阶卡恩-希利亚德方程的拟合与优化控制
IF 2 2区 数学
SIAM Journal on Mathematical Analysis Pub Date : 2024-07-09 DOI: 10.1137/24m1630372
Pierluigi Colli, Gianni Gilardi, Andrea Signori, Jürgen Sprekels
{"title":"Curvature Effects in Pattern Formation: Well-Posedness and Optimal Control of a Sixth-Order Cahn–Hilliard Equation","authors":"Pierluigi Colli, Gianni Gilardi, Andrea Signori, Jürgen Sprekels","doi":"10.1137/24m1630372","DOIUrl":"https://doi.org/10.1137/24m1630372","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4928-4969, August 2024. <br/> Abstract. This work investigates the well-posedness and optimal control of a sixth-order Cahn–Hilliard equation, a higher-order variant of the celebrated and well-established Cahn–Hilliard equation. The equation is endowed with a source term, where the control variable enters as a distributed mass regulator. The inclusion of additional spatial derivatives in the sixth-order formulation enables the model to capture curvature effects, leading to a more accurate depiction of isothermal phase separation dynamics in complex materials systems. We provide a well-posedness result for the aforementioned system when the corresponding nonlinearity of double-well shape is regular and then analyze a corresponding optimal control problem. For the latter, existence of optimal controls is established, and the first-order necessary optimality conditions are characterized via a suitable variational inequality. These results aim at contributing to improving the understanding of the mathematical properties and control aspects of the sixth-order Cahn–Hilliard equation, offering potential applications in the design and optimization of materials with tailored microstructures and properties.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"31 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572998","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
Globally Analytical Solutions of the Compressible Oldroyd-B Model Without Retardation 无缓速可压缩奥尔德罗伊德-B 模型的全局分析解决方案
IF 2 2区 数学
SIAM Journal on Mathematical Analysis Pub Date : 2024-07-05 DOI: 10.1137/23m1588974
Xinghong Pan
{"title":"Globally Analytical Solutions of the Compressible Oldroyd-B Model Without Retardation","authors":"Xinghong Pan","doi":"10.1137/23m1588974","DOIUrl":"https://doi.org/10.1137/23m1588974","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4854-4869, August 2024. <br/> Abstract. In this paper, we prove the global existence of analytical solutions to the compressible Oldroyd-B model without retardation near a nonvacuum equilibrium in [math] [math]. Zero retardation results in zero dissipation in the velocity equation, which is the main difficulty that prevents us from obtaining the long time well-posedness of solutions. Through dedicated analysis, we find that the linearized equations of this model have damping effects, which ensure the global-in-time existence of small data solutions. However, the nonlinear quadratic terms have one more order derivative than the linear part and no good structure is discovered to overcome this derivative loss problem. So we can only build the result in the analytical energy space rather than Sobolev space with finite order derivatives.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"3 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573000","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 Scattering Behavior of Corner Domains with Anisotropic Inhomogeneities 各向异性非均质角域的散射行为
IF 2 2区 数学
SIAM Journal on Mathematical Analysis Pub Date : 2024-07-05 DOI: 10.1137/23m1603029
Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
{"title":"On Scattering Behavior of Corner Domains with Anisotropic Inhomogeneities","authors":"Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian","doi":"10.1137/23m1603029","DOIUrl":"https://doi.org/10.1137/23m1603029","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4834-4853, August 2024. <br/> Abstract. This paper investigates the possible scattering and nonscattering behavior of an anisotropic and inhomogeneous Lipschitz medium at a fixed wave number and with a single incident field. We connect the anisotropic nonscattering problem to a Bernoulli type free boundary problem. By invoking methods from the theory of free boundaries, we show that an anisotropic medium with Lipschitz but not [math] boundary scatters every incident wave that satisfies a nondegeneracy condition.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573002","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
Global Classical Large Solutions for the Radiation Hydrodynamics Model in Unbounded Domains 无界域辐射流体力学模型的全局经典大解
IF 2 2区 数学
SIAM Journal on Mathematical Analysis Pub Date : 2024-07-04 DOI: 10.1137/23m1598581
Jing Wei, Minyi Zhang, Changjiang Zhu
{"title":"Global Classical Large Solutions for the Radiation Hydrodynamics Model in Unbounded Domains","authors":"Jing Wei, Minyi Zhang, Changjiang Zhu","doi":"10.1137/23m1598581","DOIUrl":"https://doi.org/10.1137/23m1598581","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4811-4833, August 2024. <br/> Abstract. This paper is concerned with the global existence of large solutions to the initial and initial boundary value problems for the radiation hydrodynamics model with constant viscosity coefficient and temperature-dependent heat conductivity coefficient. In particular, the initial data and [math] could be arbitrarily large. Compared with the classical compressible Navier–Stokes equations, the research on the radiation hydrodynamics model is more complicated due to the presence of the radiation effect. To overcome difficulties caused by the radiation, inspired by [J. Li and Z. L. Liang, Arch. Ration. Mech. Anal., 220 (2016), pp. 1195–1208; J. H. Zhang and H. J. Zhao, SIAM J. Math. Anal., 55 (2023), pp. 6229–6261], we construct a pointwise estimate between the radiative heat flux and the temperature; then we can establish the desired basic energy estimate by considering that the temperature has lower and upper bounds separately. And once that is obtained, the main result is proved by employing the elementary energy methods.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"39 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549467","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
The Calderón Problem for Space-Time Fractional Parabolic Operators with Variable Coefficients 具有可变系数的时空分数抛物线算子的卡尔德龙问题
IF 2 2区 数学
SIAM Journal on Mathematical Analysis Pub Date : 2024-07-03 DOI: 10.1137/23m1584137
Agnid Banerjee, Soumen Senapati
{"title":"The Calderón Problem for Space-Time Fractional Parabolic Operators with Variable Coefficients","authors":"Agnid Banerjee, Soumen Senapati","doi":"10.1137/23m1584137","DOIUrl":"https://doi.org/10.1137/23m1584137","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4759-4810, August 2024. <br/> Abstract. We study an inverse problem for variable coefficient fractional parabolic operators of the form [math] for [math] and show the unique recovery of [math] from exterior measured data. Similar to the fractional elliptic case, we use a Runge-type approximation argument, which is obtained via a global weak unique continuation property. The proof of such a unique continuation result involves a new Carleman estimate for the associated variable coefficient extension operator. In the latter part of the work, we prove analogous unique determination results for fractional parabolic operators with drift.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"4 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549357","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
Stability Analysis of an Extended Quadrature Method of Moments for Kinetic Equations 动力学方程的扩展正交矩法稳定性分析
IF 2 2区 数学
SIAM Journal on Mathematical Analysis Pub Date : 2024-07-02 DOI: 10.1137/23m157911x
Ruixi Zhang, Qian Huang, Wen-An Yong
{"title":"Stability Analysis of an Extended Quadrature Method of Moments for Kinetic Equations","authors":"Ruixi Zhang, Qian Huang, Wen-An Yong","doi":"10.1137/23m157911x","DOIUrl":"https://doi.org/10.1137/23m157911x","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4687-4711, August 2024. <br/> Abstract. This paper performs a stability analysis of a class of moment closure systems derived with an extended quadrature method of moments (EQMOM) for the one-dimensional Bhatnagar–Gross–Krook equation. The class is characterized with a kernel function. A sufficient condition on the kernel is identified for the EQMOM-derived moment systems to be strictly hyperbolic. We also investigate the realizability of the moment method. Moreover, sufficient and necessary conditions are established for the two-node systems to be well-defined and strictly hyperbolic and to preserve the dissipation property of the kinetic equation.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"138 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523527","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
Nonlocal Elliptic and Parabolic Equations with General Stable Operators in Weighted Sobolev Spaces 加权索波列夫空间中具有一般稳定算子的非局部椭圆和抛物方程
IF 2 2区 数学
SIAM Journal on Mathematical Analysis Pub Date : 2024-07-02 DOI: 10.1137/23m160061x
Hongjie Dong, Junhee Ryu
{"title":"Nonlocal Elliptic and Parabolic Equations with General Stable Operators in Weighted Sobolev Spaces","authors":"Hongjie Dong, Junhee Ryu","doi":"10.1137/23m160061x","DOIUrl":"https://doi.org/10.1137/23m160061x","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4623-4661, August 2024. <br/> Abstract. We study nonlocal elliptic and parabolic equations on [math] open sets in weighted Sobolev spaces, where [math]. The operators we consider are infinitesimal generators of symmetric stable Lévy processes, whose Lévy measures are allowed to be very singular. Additionally, for parabolic equations, the measures are assumed to be merely measurable in the time variable.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"23 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523593","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
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