Studies in Applied Mathematics最新文献

{"title":"Asymptotic Behaviors of Chandrasekhar Variational Problem for Neutron Stars With Slater-Type Modification","authors":"Deke Li, Qingxuan Wang","doi":"10.1111/sapm.70058","DOIUrl":"https://doi.org/10.1111/sapm.70058","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we consider the Chandrasekhar variational model for neutron stars with defocusing Slater-type modifications. First, we show the existence and nonexistence of the ground state <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ρ</mi>\u0000 <mi>ε</mi>\u0000 </msub>\u0000 <annotation>$rho _{varepsilon }$</annotation>\u0000 </semantics></math> by concentration–compactness method, and particularly use two auxiliary functions to prove the strongly binding inequality. Second, we characterize perturbation limit behaviors of ground states <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ρ</mi>\u0000 <mi>ε</mi>\u0000 </msub>\u0000 <annotation>$rho _{varepsilon }$</annotation>\u0000 </semantics></math> as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ε</mi>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mn>0</mn>\u0000 <mo>+</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$varepsilon rightarrow 0^+$</annotation>\u0000 </semantics></math> and obtain two different blow-up profiles corresponding to two limit equations for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mo>∗</mo>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$N= N_*$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>></mo>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mo>∗</mo>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$N> N_*$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>ε</mi>\u0000 <annotation>$varepsilon$</annotation>\u0000 </semantics></math> is a parameter corresponding to Slater-type modifications, and <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mo>∗</mo>\u0000 </msub>\u0000 <annotation>$N_*$</annotation>\u0000 </semantics></math> is a threshold value related to the <i>Chandrasekhar limit</i>. Finally, we study the limit behaviors for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>≥</mo>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mo>∗</mo>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$Nge N_*$</annotation>\u0000 </semantics></math> as <span></span><math>\u0000 <semantics>\u0000 <m","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950103","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}

{"title":"On the Coupled Maxwell–Bloch System of Equations With Nondecaying Fields at Infinity","authors":"Sitai Li,&nbsp;Gino Biondini,&nbsp;Gregor Kovačič","doi":"10.1111/sapm.70055","DOIUrl":"https://doi.org/10.1111/sapm.70055","url":null,"abstract":"<div>\u0000 \u0000 <p>We study an initial-boundary-value problem (IBVP) for a system of coupled Maxwell–Bloch equations (CMBE) that model two colors or polarizations of light resonantly interacting with a degenerate, two-level, active optical medium with an excited state and a pair of degenerate ground states. We assume that the electromagnetic field approaches nonvanishing plane waves in the far past and future. This type of interaction has been found to underlie nonlinear optical phenomena including electromagnetically induced transparency, slow light, stopped light, and quantum memory. Under the assumptions of unidirectional, lossless propagation of slowly modulated plane waves, the resulting CMBE become completely integrable in the sense of possessing a Lax pair. In this paper, we formulate an inverse scattering transform (IST) corresponding to these CMBE and their Lax pair, allowing for the spectral line of the atomic transitions in the active medium to have a finite width. The scattering problem for this Lax pair is the same as for the Manakov system. The main advancement in this IST for CMBE is calculating the nontrivial spatial propagation of the spectral data and determining the state of the optical medium in the distant future from that in the distant past, which is needed for the complete formulation of the IBVP. The Riemann–Hilbert problem is used to extract the spatio-temporal dependence of the solution from the evolving spectral data. We further derive and analyze several types of solitons and determine their velocity and stability, as well as find dark states of the medium, which fail to interact with a given pulse.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950102","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}

{"title":"Derivation of the Bacterial Run-and-Tumble Kinetic Model: Quantitative and Strong Convergence Results","authors":"Alain Blaustein","doi":"10.1111/sapm.70060","DOIUrl":"https://doi.org/10.1111/sapm.70060","url":null,"abstract":"<p>During the past century, biologists and mathematicians investigated two mechanisms underlying bacteria motion: the run phase during which bacteria move in straight lines and the tumble phase in which they change their orientation. When surrounded by a chemical attractant, experiments show that bacteria increase their run time as moving up concentration gradients, leading to a biased random walk toward favorable regions. This observation raises the following question, which has drawn intense interest from both biological and mathematical communities: what cellular mechanisms enable bacteria to feel concentration gradients? In this article, we investigate an asymptotic regime that was proposed to explain this ability thanks to internal mechanisms. More precisely, we derive the run-and-tumble kinetic equation with concentration's gradient-dependent tumbling rate from a more comprehensive model, which incorporates internal cellular mechanisms. Our result improves on previous investigations, as we obtain strong convergence toward the gradient-dependent kinetic model with quantitative and formally optimal convergence rates. The main ingredient consists in identifying a set of coordinates for the internal cellular dynamics in which concentration gradients arise explicitly. Then, we use relative entropy methods in order to capture quantitative measurement of the distance between the model incorporating cellular mechanisms and the one with concentration-gradient-dependent tumbling rate.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70060","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Separation of the Initial Conditions in the Inverse Problem for One-Dimensional Nonlinear Tsunami Wave Run-Up Theory","authors":"Alexei Rybkin,&nbsp;Oleksandr Bobrovnikov,&nbsp;Noah Palmer,&nbsp;Daniel Abramowicz,&nbsp;Efim Pelinovsky","doi":"10.1111/sapm.70054","DOIUrl":"https://doi.org/10.1111/sapm.70054","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;We investigate the inverse tsunami wave problem within the framework of the one-dimensional (1D) nonlinear shallow water equations (SWE). Specifically, we show that the initial displacement &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;η&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$eta _0(x)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and velocity &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$u_0(x)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of the wave can be recovered, given the known motion of the shoreline &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$R(t)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (the wet/dry free boundary), in terms of the Abel transform. We demonstrate that for power-shaped inclined bathymetries, this problem admits a complete solution for any &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;η&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$eta _0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$u_0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, provided the wave does not break.&lt;/p&gt;\u0000 &lt;p&gt;It is important to note that, in contrast to the direct problem (also known as the tsunami wave run-up problem), where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$R(t)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; can be computed exactly only for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143919783","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}

{"title":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.70056","DOIUrl":"https://doi.org/10.1111/sapm.70056","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70056","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143919782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic Properties of Special Function Solutions of the Painlevé III Equation for Fixed Parameters","authors":"Hao Pan,&nbsp;Andrei Prokhorov","doi":"10.1111/sapm.70051","DOIUrl":"https://doi.org/10.1111/sapm.70051","url":null,"abstract":"<p>In this paper, we compute the small and large <span></span><math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math> asymptotics of the special function solutions of the Painlevé-III equation in the complex plane. We use the representation in terms of Toeplitz determinants of Bessel functions obtained by Masuda. Toeplitz determinants are rewritten as multiple contour integrals using Andrèief's identity. The small and large <span></span><math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math> asymptotics are obtained using elementary asymptotic methods applied to the multiple contour integral. The asymptotics is extended to the whole complex plane using analytic continuation formulas for Bessel functions. The claimed result has not appeared in the literature before. We note that the Toeplitz determinant representation is useful for numerical computations of corresponding solutions of the Painlevé-III equation.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70051","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143861851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Preface: Recent Advances in the Analysis and Simulation of Compressible Flow Problems: The 75th Anniversary of the Landmark Report by Lagerstrom, Cole, and Trilling (1949)#","authors":"Pedro M. Jordan,&nbsp;James V. Lambers,&nbsp;Bailey Rester","doi":"10.1111/sapm.70052","DOIUrl":"https://doi.org/10.1111/sapm.70052","url":null,"abstract":"<div>\u0000 \u0000 <p>This special issue of <i>Studies in Applied Mathematics</i> commemorates the 75th anniversary of the publication of the highly influential 1949 “GALCIT” report by Lagerstrom, Cole, and Trilling, a work which helped usher in the modern era of compressible flow studies. Herein, a collection of papers highlighting recent advances in the treatment of topics/problems relating to both lossless and dissipative compressible flow phenomena is presented.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143846131","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}

{"title":"Augmented Total Variation Regularization in Radon-Type Inverse Problems","authors":"Nicholas E. Protonotarios,&nbsp;Nikolaos Dikaios,&nbsp;Dimosthenis Kaponis,&nbsp;Antonios Charalambopoulos","doi":"10.1111/sapm.70053","DOIUrl":"https://doi.org/10.1111/sapm.70053","url":null,"abstract":"<p>We introduce the augmented total variation (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation>$TV$</annotation>\u0000 </semantics></math>) regularization method for Radon-type inverse problems. Our novel approach incorporates a dual variable into the regularization process, thereby extending and essentially augmenting traditional <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation>$TV$</annotation>\u0000 </semantics></math> regularization techniques. The proposed method is robust, requiring only one algorithmic iteration to achieve accurate reconstructions. Numerical experiments on a modified Shepp–Logan phantom demonstrate that the augmented <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation>$TV$</annotation>\u0000 </semantics></math> regularization consistently yields higher structural similarity index metric (SSIM) values and lower mean absolute difference (MAD) values compared to filtered backprojection and standard <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation>$TV$</annotation>\u0000 </semantics></math> regularization. These findings indicate that our method not only reduces reconstruction errors but also preserves structural details.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70053","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143846004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Asymptotic Behaviors of Acoustic Waves Due to High-Contrast Material Inclusions","authors":"Yueguang Hu,&nbsp;Hongyu Liu","doi":"10.1111/sapm.70048","DOIUrl":"https://doi.org/10.1111/sapm.70048","url":null,"abstract":"<p>This paper investigates the asymptotic behaviors of time-harmonic acoustic waves generated by an incident wave illuminating inhomogeneous medium inclusions with high-contrast material parameters. We derive sharp asymptotic estimates and obtain several effective acoustic obstacle scattering models when the material parameters take extreme values. The results clarify the connection between inhomogeneous medium scattering and obstacle scattering for acoustic waves, providing a clear criterion for identifying the boundary conditions of acoustic obstacles in practice. The contributions of this paper are twofold. First, we provide a rigorous mathematical characterization of the classical sound-hard and sound-soft obstacle scattering models. We demonstrate that a sound-hard obstacle can be viewed as an inhomogeneous medium inclusion with infinite mass density, while a sound-soft obstacle corresponds to an inclusion with zero mass density and zero bulk modulus. Second, we introduce two novel acoustic obstacle scattering models when the mass density of the inclusion degenerates to zero. These new models offer a fresh perspective on considering inhomogeneous medium inclusions with high-contrast material parameters.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70048","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Large Deviation Principles of Fractional Stochastic Nonclassical Diffusion Equations on Unbounded Domains","authors":"Zhang Chen,&nbsp;Bixiang Wang,&nbsp;Dandan Yang","doi":"10.1111/sapm.70042","DOIUrl":"https://doi.org/10.1111/sapm.70042","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study the large deviation principle (LDP) of the fractional stochastic nonclassical diffusion equation with superlinear drift driven by nonlinear noise defined on unbounded domains. We first prove the well-posedness and the strong convergence of solutions of the corresponding control equation with respect to control in the weak topology. We then prove the convergence in probability of solutions of the stochastic equation as the noise intensity approaches zero, and finally establish the LDP of the stochastic equation by the weak convergence method. The noncompactness of Sobolev embeddings on unbounded domains is overcome by the uniform tail-ends estimates on the solutions of the control equation.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143831309","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}