Javier A. Almonacid, Sebastián A. Domínguez-Rivera, Ryan N. Konno, Nilima Nigam, Stephanie A. Ross, Cassidy Tam, James M. Wakeling
SIAM Journal on Applied Mathematics, Ahead of Print. Abstract. Skeletal muscles are living tissues that can undergo large deformations in short periods of time and that can be activated to produce force. In this paper we use the principles of continuum mechanics to propose a dynamic, fully nonlinear, and three-dimensional model to describe the deformation of these tissues. We model muscles as a fiber-reinforced composite and transversely isotropic material. We introduce a flexible computational framework to approximate the deformations of skeletal muscle to provide new insights into the underlying mechanics of these tissues. The model parameters and mechanical properties are obtained through experimental data and can be specified locally. A semi-implicit in-time, conforming, finite element in space scheme is used to approximate the solutions to the governing nonlinear dynamic model. We provide a series of numerical experiments demonstrating the application of this framework to relevant problems in biomechanics and also discuss questions around model validation.
{"title":"A Three-Dimensional Model of Skeletal Muscle Tissues","authors":"Javier A. Almonacid, Sebastián A. Domínguez-Rivera, Ryan N. Konno, Nilima Nigam, Stephanie A. Ross, Cassidy Tam, James M. Wakeling","doi":"10.1137/22m1506985","DOIUrl":"https://doi.org/10.1137/22m1506985","url":null,"abstract":"SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Skeletal muscles are living tissues that can undergo large deformations in short periods of time and that can be activated to produce force. In this paper we use the principles of continuum mechanics to propose a dynamic, fully nonlinear, and three-dimensional model to describe the deformation of these tissues. We model muscles as a fiber-reinforced composite and transversely isotropic material. We introduce a flexible computational framework to approximate the deformations of skeletal muscle to provide new insights into the underlying mechanics of these tissues. The model parameters and mechanical properties are obtained through experimental data and can be specified locally. A semi-implicit in-time, conforming, finite element in space scheme is used to approximate the solutions to the governing nonlinear dynamic model. We provide a series of numerical experiments demonstrating the application of this framework to relevant problems in biomechanics and also discuss questions around model validation.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"3 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882290","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 856-889, June 2024. Abstract. The Gray–Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio-temporal structures, including pulses, spots, stripes, and self-replicating patterns. We consider an extension of this model in which the spread of the different chemicals is assumed to be nonlocal and can thus be represented by an integral operator. In particular, we focus on the case of strictly positive, symmetric, [math] convolution kernels that have a finite second moment. Modeling the equations on a finite interval, we prove the existence of small-time weak solutions in the case of nonlocal Dirichlet and Neumann boundary constraints. We then use this result to develop a finite element numerical scheme that helps us explore the effects of nonlocal diffusion on the formation of pulse solutions.
{"title":"Analysis and Simulation of a Nonlocal Gray–Scott Model","authors":"Loic Cappanera, Gabriela Jaramillo, Cory Ward","doi":"10.1137/22m1542441","DOIUrl":"https://doi.org/10.1137/22m1542441","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 856-889, June 2024. <br/>Abstract. The Gray–Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio-temporal structures, including pulses, spots, stripes, and self-replicating patterns. We consider an extension of this model in which the spread of the different chemicals is assumed to be nonlocal and can thus be represented by an integral operator. In particular, we focus on the case of strictly positive, symmetric, [math] convolution kernels that have a finite second moment. Modeling the equations on a finite interval, we prove the existence of small-time weak solutions in the case of nonlocal Dirichlet and Neumann boundary constraints. We then use this result to develop a finite element numerical scheme that helps us explore the effects of nonlocal diffusion on the formation of pulse solutions.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"47 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882515","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 890-914, June 2024. Abstract. We consider an [math]-periodic ([math]) tubular structure, modeled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on [math] which is fourth order at a discrete set of values of the magnetic potential (critical points) and second order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence is also estimated. This represents a physically viable model of a phase transition as the strength of the (constant) magnetic field increases.
{"title":"Phase Transition in a Periodic Tubular Structure","authors":"Alexander V. Kiselev, Kirill Ryadovkin","doi":"10.1137/23m157274x","DOIUrl":"https://doi.org/10.1137/23m157274x","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 890-914, June 2024. <br/> Abstract. We consider an [math]-periodic ([math]) tubular structure, modeled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on [math] which is fourth order at a discrete set of values of the magnetic potential (critical points) and second order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence is also estimated. This represents a physically viable model of a phase transition as the strength of the (constant) magnetic field increases.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"20 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882314","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}
L. Baldassari, M. V. de Hoop, E. Francini, S. Vessella
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 831-855, June 2024. Abstract. Through coupled physics, we study an early-warning inverse source problem for the constant-coefficient elasto-gravitational equations. It consists of a mixed hyperbolic-elliptic system of partial differential equations describing elastic wave displacement and gravity perturbations produced by a source in a homogeneous bounded medium. Within the Cowling approximation, we prove uniqueness and Lipschitz stability for the inverse problem of recovering the moment tensor and the location of the source from early-time measurements of the changes of the gravitational field. The setup studied in this paper is motivated by gravity-based earthquake early warning systems, which are gaining much attention recently.
{"title":"Early-Warning Inverse Source Problem for the Elasto-Gravitational Equations","authors":"L. Baldassari, M. V. de Hoop, E. Francini, S. Vessella","doi":"10.1137/23m1564651","DOIUrl":"https://doi.org/10.1137/23m1564651","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 831-855, June 2024. <br/> Abstract. Through coupled physics, we study an early-warning inverse source problem for the constant-coefficient elasto-gravitational equations. It consists of a mixed hyperbolic-elliptic system of partial differential equations describing elastic wave displacement and gravity perturbations produced by a source in a homogeneous bounded medium. Within the Cowling approximation, we prove uniqueness and Lipschitz stability for the inverse problem of recovering the moment tensor and the location of the source from early-time measurements of the changes of the gravitational field. The setup studied in this paper is motivated by gravity-based earthquake early warning systems, which are gaining much attention recently.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"36 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833290","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 808-830, June 2024. Abstract. We study waves on infinite one-dimensional lattices of particles that each interact with all others through power-law forces [math]. The inverse-cube case corresponds to Calogero–Moser systems which are well known to be completely integrable for any finite number of particles. The formal long-wave limit for unidirectional waves in these lattices is the Korteweg–de Vries equation if [math], but with [math] it is a nonlocal dispersive PDE that reduces to the Benjamin–Ono equation for [math]. For the infinite Calogero–Moser lattice, we find explicit formulas that describe solitary and periodic traveling waves.
{"title":"On Long Waves and Solitons in Particle Lattices with Forces of Infinite Range","authors":"Benjamin Ingimarson, Robert L. Pego","doi":"10.1137/23m1607209","DOIUrl":"https://doi.org/10.1137/23m1607209","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 808-830, June 2024. <br/> Abstract. We study waves on infinite one-dimensional lattices of particles that each interact with all others through power-law forces [math]. The inverse-cube case corresponds to Calogero–Moser systems which are well known to be completely integrable for any finite number of particles. The formal long-wave limit for unidirectional waves in these lattices is the Korteweg–de Vries equation if [math], but with [math] it is a nonlocal dispersive PDE that reduces to the Benjamin–Ono equation for [math]. For the infinite Calogero–Moser lattice, we find explicit formulas that describe solitary and periodic traveling waves.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"36 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833362","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 783-807, June 2024. Abstract. Evidence shows that resource quality can determine the costs and benefits of the fear effect on consumer dynamics. However, mechanistic modeling and analysis are lacking. This paper formulates a tritrophic level food chain model that integrates both stoichiometric food quality and fear effect. We establish the well-posedness of the model and examine the existence and stability of equilibria. Through extensive numerical simulations, we validate our findings and visually explore the interactive effects of fear and food quality. Our results reveal that the fear effect from predators stabilizes the system. Furthermore, we demonstrate that the fear effect amplifies the influence of food quality on consumers. When food quality is favorable, the fear effect enhances consumer production efficiency, whereas, in the case of poor food quality, the fear effect exacerbates the decline in production efficiency caused by low-nutrient food.
{"title":"Stoichiometry-Dependent Fear Effect in a Food Chain Model","authors":"Tianxu Wang, Hao Wang","doi":"10.1137/23m1581613","DOIUrl":"https://doi.org/10.1137/23m1581613","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 783-807, June 2024. <br/>Abstract. Evidence shows that resource quality can determine the costs and benefits of the fear effect on consumer dynamics. However, mechanistic modeling and analysis are lacking. This paper formulates a tritrophic level food chain model that integrates both stoichiometric food quality and fear effect. We establish the well-posedness of the model and examine the existence and stability of equilibria. Through extensive numerical simulations, we validate our findings and visually explore the interactive effects of fear and food quality. Our results reveal that the fear effect from predators stabilizes the system. Furthermore, we demonstrate that the fear effect amplifies the influence of food quality on consumers. When food quality is favorable, the fear effect enhances consumer production efficiency, whereas, in the case of poor food quality, the fear effect exacerbates the decline in production efficiency caused by low-nutrient food.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"62 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833330","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 756-781, April 2024. Abstract. We study nematic configurations within three-dimensional (3D) cuboids, with planar degenerate boundary conditions on the cuboid faces, in the Landau–de Gennes framework. There are two geometry-dependent variables: the edge length of the square cross-section, [math], and the parameter [math], which is a measure of the cuboid height. Theoretically, we prove the existence and uniqueness of the global minimizer with a small enough cuboid size. We develop a new numerical scheme for the high-index saddle dynamics to deal with the surface energies. We report on a plethora of (meta)stable states, and their dependence on [math] and [math], and in particular how the 3D states are connected with their two-dimensional counterparts on squares and rectangles. Notably, we find families of almost uniaxial stable states constructed from the topological classification of tangent unit-vector fields and study transition pathways between them. We also provide a phase diagram of competing (meta)stable states as a function of [math] and [math].
{"title":"Multistability for Nematic Liquid Crystals in Cuboids with Degenerate Planar Boundary Conditions","authors":"Baoming Shi, Yucen Han, Apala Majumdar, Lei Zhang","doi":"10.1137/23m1604606","DOIUrl":"https://doi.org/10.1137/23m1604606","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 756-781, April 2024. <br/> Abstract. We study nematic configurations within three-dimensional (3D) cuboids, with planar degenerate boundary conditions on the cuboid faces, in the Landau–de Gennes framework. There are two geometry-dependent variables: the edge length of the square cross-section, [math], and the parameter [math], which is a measure of the cuboid height. Theoretically, we prove the existence and uniqueness of the global minimizer with a small enough cuboid size. We develop a new numerical scheme for the high-index saddle dynamics to deal with the surface energies. We report on a plethora of (meta)stable states, and their dependence on [math] and [math], and in particular how the 3D states are connected with their two-dimensional counterparts on squares and rectangles. Notably, we find families of almost uniaxial stable states constructed from the topological classification of tangent unit-vector fields and study transition pathways between them. We also provide a phase diagram of competing (meta)stable states as a function of [math] and [math].","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"32 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805645","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 732-755, April 2024. Abstract. We study a diffusive Susceptible-Infected-Susceptible (SIS) epidemic model with the mass-action transmission mechanism and show, under appropriate assumptions on the parameters, the existence of multiple endemic equilibria (EE). Our results answer some open questions on previous studies related to disease extinction or persistence when [math] and the multiplicity of EE solutions when [math]. Interestingly, even with such a simple nonlinearity induced by the mass-action, we show that the diffusive epidemic model may have an S-shaped or backward bifurcation curve of EE solutions. This strongly highlights the impacts of environmental heterogeneity on the spread of infectious diseases as the basic reproduction number alone is insufficient as a threshold quantity to predict its extinction. Our results also shed some light on the significance of disease transmission mechanisms.
SIAM 应用数学杂志》第 84 卷第 2 期第 732-755 页，2024 年 4 月。 摘要。我们研究了一个具有大规模作用传播机制的扩散性易感-感染-易感（SIS）流行病模型，并证明在适当的参数假设下，存在多个流行病均衡（EE）。我们的结果回答了以往研究中的一些公开问题，这些问题涉及当[math]时疾病的灭绝或持续以及当[math]时 EE 解的多重性。有趣的是，即使由质量作用引起的非线性如此简单，我们仍然发现扩散流行病模型的 EE 解可能呈 S 形或向后分叉曲线。这有力地凸显了环境异质性对传染病传播的影响，因为仅凭基本繁殖数量不足以作为预测其灭绝的临界量。我们的研究结果还揭示了疾病传播机制的重要性。
{"title":"Multiplicity of Endemic Equilibria for a Diffusive SIS Epidemic Model with Mass-Action","authors":"Keoni Castellano, Rachidi B. Salako","doi":"10.1137/23m1613888","DOIUrl":"https://doi.org/10.1137/23m1613888","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 732-755, April 2024. <br/> Abstract. We study a diffusive Susceptible-Infected-Susceptible (SIS) epidemic model with the mass-action transmission mechanism and show, under appropriate assumptions on the parameters, the existence of multiple endemic equilibria (EE). Our results answer some open questions on previous studies related to disease extinction or persistence when [math] and the multiplicity of EE solutions when [math]. Interestingly, even with such a simple nonlinearity induced by the mass-action, we show that the diffusive epidemic model may have an S-shaped or backward bifurcation curve of EE solutions. This strongly highlights the impacts of environmental heterogeneity on the spread of infectious diseases as the basic reproduction number alone is insufficient as a threshold quantity to predict its extinction. Our results also shed some light on the significance of disease transmission mechanisms.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"176 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613108","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 710-731, April 2024. Abstract. The creation of hairpin or lambda vortices, typical for the early stages of the laminar-turbulent transition process in various boundary layer flows, in some sense may be associated with blow-up solutions of the Fisher–Kolmogorov–Petrovsky–Piskunov equation. In contrast to the usual applications of this nonlinear evolution equation of the reaction-diffusion type, the solution quantity in the present context needs to stay neither bounded nor positive. We focus on the solution behavior beyond a finite-time point blow-up event, which consists of two moving singularities (representing the cores of the vortex legs) propagating in opposite directions, and their initial motion is determined with the method of matched asymptotic expansions. After resolving subtleties concerning the transition between logarithmic and algebraic expansion terms regarding asymptotic layers, we find that the internal singularity structure resembles a combination of second- and first-order poles in the form of a singular traveling wave with a time-dependent speed imprinted through the characteristics of the preceding blow-up event.
{"title":"Moving Singularities of the Forced Fisher–KPP Equation: An Asymptotic Approach","authors":"Markus Kaczvinszki, Stefan Braun","doi":"10.1137/23m1552905","DOIUrl":"https://doi.org/10.1137/23m1552905","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 710-731, April 2024. <br/> Abstract. The creation of hairpin or lambda vortices, typical for the early stages of the laminar-turbulent transition process in various boundary layer flows, in some sense may be associated with blow-up solutions of the Fisher–Kolmogorov–Petrovsky–Piskunov equation. In contrast to the usual applications of this nonlinear evolution equation of the reaction-diffusion type, the solution quantity in the present context needs to stay neither bounded nor positive. We focus on the solution behavior beyond a finite-time point blow-up event, which consists of two moving singularities (representing the cores of the vortex legs) propagating in opposite directions, and their initial motion is determined with the method of matched asymptotic expansions. After resolving subtleties concerning the transition between logarithmic and algebraic expansion terms regarding asymptotic layers, we find that the internal singularity structure resembles a combination of second- and first-order poles in the form of a singular traveling wave with a time-dependent speed imprinted through the characteristics of the preceding blow-up event.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"57 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593502","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 687-709, April 2024. Abstract. This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and uniqueness of solutions. The stability estimates are deduced for the inverse source problems, which aim to determine the strength of the random source. To enhance the stability of the inverse source problems, we incorporate a priori information regarding the regularity and support of the strength. In the case of homogeneous media, a Hölder stability estimate is established, providing a quantitative measure of the stability for reconstructing the source strength. For the more challenging scenario of inhomogeneous media, a logarithmic stability estimate is presented, capturing the intricate interactions between the source and the varying medium properties.
{"title":"Stability for Inverse Source Problems of the Stochastic Helmholtz Equation with a White Noise","authors":"Peijun Li, Ying Liang","doi":"10.1137/23m1586331","DOIUrl":"https://doi.org/10.1137/23m1586331","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 687-709, April 2024. <br/> Abstract. This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and uniqueness of solutions. The stability estimates are deduced for the inverse source problems, which aim to determine the strength of the random source. To enhance the stability of the inverse source problems, we incorporate a priori information regarding the regularity and support of the strength. In the case of homogeneous media, a Hölder stability estimate is established, providing a quantitative measure of the stability for reconstructing the source strength. For the more challenging scenario of inhomogeneous media, a logarithmic stability estimate is presented, capturing the intricate interactions between the source and the varying medium properties.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"42 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593599","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}
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