The article proposes a causal five-field formulation of dissipative relativistic fluid dynamics as a quasilinear symmetric hyperbolic system of second order. The system is determined by four dissipation coefficients η , ζ , κ , μ eta ,zeta ,kappa ,mu , free functions of the fields, which quantify shear viscosity, bulk viscosity, heat conductivity, and diffusion.
{"title":"A causal formulation of dissipative relativistic fluid dynamics with or without diffusion","authors":"H. Freistuhler","doi":"10.1090/qam/1656","DOIUrl":"https://doi.org/10.1090/qam/1656","url":null,"abstract":"The article proposes a causal five-field formulation of dissipative relativistic fluid dynamics as a quasilinear symmetric hyperbolic system of second order. The system is determined by four dissipation coefficients \u0000\u0000 \u0000 \u0000 η\u0000 ,\u0000 ζ\u0000 ,\u0000 κ\u0000 ,\u0000 μ\u0000 \u0000 eta ,zeta ,kappa ,mu\u0000 \u0000\u0000, free functions of the fields, which quantify shear viscosity, bulk viscosity, heat conductivity, and diffusion.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45474269","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}
We study the evolution of vortex sheets according to the Birkhoff-Rott equation, which describe the motion of sharp shear interfaces governed by the incompressible Euler equation in two dimensions. In a recent work, the authors demonstrated within this context a marginal linear stability of circular vortex sheets, standing in sharp contrast with classical instability of the flat vortex sheet, which is known as the Kelvin-Helmholtz instability. This article continues that analysis by investigating how non-linear effects induce singularity formation near the circular vortex sheet. In high-frequency regimes, the singularity formation is primarily driven by a complex-valued, conjugated Burgers equation, which we study by modifying a classical argument from hyperbolic conservation laws. This provides a deeper understanding of the mechanisms driving the breakdown of circular vortex sheets, which are observed both numerically and experimentally.
{"title":"Non-linear singularity formation for circular vortex sheets","authors":"Ryan W. Murray, Galen Wilcox","doi":"10.1090/qam/1659","DOIUrl":"https://doi.org/10.1090/qam/1659","url":null,"abstract":"We study the evolution of vortex sheets according to the Birkhoff-Rott equation, which describe the motion of sharp shear interfaces governed by the incompressible Euler equation in two dimensions. In a recent work, the authors demonstrated within this context a marginal linear stability of circular vortex sheets, standing in sharp contrast with classical instability of the flat vortex sheet, which is known as the Kelvin-Helmholtz instability. This article continues that analysis by investigating how non-linear effects induce singularity formation near the circular vortex sheet. In high-frequency regimes, the singularity formation is primarily driven by a complex-valued, conjugated Burgers equation, which we study by modifying a classical argument from hyperbolic conservation laws. This provides a deeper understanding of the mechanisms driving the breakdown of circular vortex sheets, which are observed both numerically and experimentally.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42011968","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}
The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of traveling waves to shocks. The problem is recast as a Hamiltonian system with small friction, and an analysis of the length of oscillations yields convergence in the moderate dispersion regime ε , δ → 0 varepsilon , delta to 0 with δ = o ( ε ) delta = o(varepsilon ) , under hypotheses that the limiting shock is admissible according to the Liu E-condition and is not a contact discontinuity at either end state. A similar convergence result is proved for traveling waves of the quantum hydrodynamic system with artificial viscosity as well as for a viscous Peregrine-Boussinesq system where traveling waves model undular bores, in all cases in the moderate dispersion regime.
其目的是评估中等分散状态下扩散和分散对冲击的综合影响。对于一维弹性（或p-系统）方程的扩散色散近似，我们研究了行波对冲击的收敛性。该问题被重新定义为具有小摩擦的哈密顿系统，并且对振荡长度的分析产生了在中等色散区ε，δ的收敛性→ 0varepsilon， delta to 0，δ=o（ε） delta=o（ varepsilo），假设极限冲击根据Liu E条件是可容许的，并且在任何末端状态都不是接触不连续性。对于具有人工粘性的量子流体动力学系统的行波以及粘性Peregrine-Boussinesq系统，证明了类似的收敛结果，其中行波在所有情况下都模拟了中等色散状态下的非圆形孔。
{"title":"Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics","authors":"Daria Bolbot, D. Mitsotakis, A. Tzavaras","doi":"10.1090/qam/1658","DOIUrl":"https://doi.org/10.1090/qam/1658","url":null,"abstract":"The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of traveling waves to shocks. The problem is recast as a Hamiltonian system with small friction, and an analysis of the length of oscillations yields convergence in the moderate dispersion regime \u0000\u0000 \u0000 \u0000 ε\u0000 ,\u0000 δ\u0000 →\u0000 0\u0000 \u0000 varepsilon , delta to 0\u0000 \u0000\u0000 with \u0000\u0000 \u0000 \u0000 δ\u0000 =\u0000 o\u0000 (\u0000 ε\u0000 )\u0000 \u0000 delta = o(varepsilon )\u0000 \u0000\u0000, under hypotheses that the limiting shock is admissible according to the Liu E-condition and is not a contact discontinuity at either end state. A similar convergence result is proved for traveling waves of the quantum hydrodynamic system with artificial viscosity as well as for a viscous Peregrine-Boussinesq system where traveling waves model undular bores, in all cases in the moderate dispersion regime.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44575542","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}
This article is a brief survey of mathematical work, joint with Yilun Wu and Juhi Jang, on models of stars and galaxies. It is a sequel to the survey article by Yilun Wu [Quart. Appl. Math. 78 (2020), pp. 147–159]. The models consider rotating stars (or galaxies or gaseous planets) as composed of particles subject to gravity. Under appropriate conditions, global families of isentropic steadily rotating stars are shown to exist. Local families are also shown to exist even in the presence of variable entropy and arbitrary axisymmetric angular velocity.
{"title":"Continua of steadily rotating stars","authors":"W. Strauss","doi":"10.1090/qam/1641","DOIUrl":"https://doi.org/10.1090/qam/1641","url":null,"abstract":"This article is a brief survey of mathematical work, joint with Yilun Wu and Juhi Jang, on models of stars and galaxies. It is a sequel to the survey article by Yilun Wu [Quart. Appl. Math. 78 (2020), pp. 147–159]. The models consider rotating stars (or galaxies or gaseous planets) as composed of particles subject to gravity. Under appropriate conditions, global families of isentropic steadily rotating stars are shown to exist. Local families are also shown to exist even in the presence of variable entropy and arbitrary axisymmetric angular velocity.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49092429","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}
We are concerned with the minimal entropy conditions for one-dimensional scalar conservation laws with general convex flux functions. For such scalar conservation laws, we prove that a single entropy-entropy flux pair (η(u),q(u))(eta (u),q(u)) with η(u)eta (u) of strict convexity is sufficient to single out an entropy solution from a broad class of weak solutions in Lloc∞L^infty _{mathrm { loc}} that satisfy the inequality: η(u)t+q(u
我们研究了具有一般凸通量函数的一维标量守恒定律的最小熵条件。对于这种标量守恒定律，我们证明了单个熵熵通量对（η（u），q（u））（eta（u），q（u））与严格凸性的η（u）x≤μeta（u）_t+q（u）_xleqmu。此外，我们基于通量函数f（u）f（u）和熵函数η（u）eta（u）在无穷大处的渐近行为，将这一结果推广到L L o c p L ^ p｛mathrm｛loc｝｝中的一类弱解。这些证明基于一维标量守恒定律的熵解和相应的Hamilton-Jacobi方程的粘性解之间的等价性，以及补偿紧致性理论中类似使用的双线性形式和换向器估计。
{"title":"Minimal entropy conditions for scalar conservation laws with general convex fluxes","authors":"G. Cao, Guifang Chen","doi":"10.1090/qam/1669","DOIUrl":"https://doi.org/10.1090/qam/1669","url":null,"abstract":"<p>We are concerned with the minimal entropy conditions for one-dimensional scalar conservation laws with general convex flux functions. For such scalar conservation laws, we prove that a single entropy-entropy flux pair <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis eta left-parenthesis u right-parenthesis comma q left-parenthesis u right-parenthesis right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>η<!-- η --></mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(eta (u),q(u))</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> with <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"eta left-parenthesis u right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>η<!-- η --></mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">eta (u)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of strict convexity is sufficient to single out an entropy solution from a broad class of weak solutions in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Subscript normal l normal o normal c Superscript normal infinity\">\u0000 <mml:semantics>\u0000 <mml:msubsup>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">l</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">o</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">c</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 </mml:msubsup>\u0000 <mml:annotation encoding=\"application/x-tex\">L^infty _{mathrm { loc}}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> that satisfy the inequality: <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"eta left-parenthesis u right-parenthesis Subscript t Baseline plus q left-parenthesis u right-parenthesis Subscript x Baseline less-than-or-equal-to mu\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>η<!-- η --></mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>q</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:msu","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43395378","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}
We extend the scope of our recent Compensated Integrability theory, by exploiting the multi-linearity of the determinant map over S y m n ( R ) mathbf {Sym}_n(mathbb {R}) . This allows us to establish new a priori estimates for inviscid gases flowing in the whole space R d mathbb {R}^d . Notably, we estimate the defect measure (Boltzman equation) or weighted spacial correlations of the velocity field (Euler system). As usual, our bounds involve only the total mass and energy of the flow.
通过利用Sym n(R) mathbf {Sym}_n(mathbb {R})上的行列式映射的多重线性，我们扩展了我们最近的补偿可积性理论的范围。这使我们能够对在整个空间R d mathbb {R}^d中流动的无粘性气体建立新的先验估计。值得注意的是，我们估计了缺陷度量(玻尔兹曼方程)或速度场的加权空间相关性(欧拉系统)。像往常一样，我们的边界只涉及流的总质量和总能量。
{"title":"Mixed determinants, compensated integrability, and new a priori estimates in gas dynamics","authors":"D. Serre","doi":"10.1090/qam/1640","DOIUrl":"https://doi.org/10.1090/qam/1640","url":null,"abstract":"We extend the scope of our recent Compensated Integrability theory, by exploiting the multi-linearity of the determinant map over \u0000\u0000 \u0000 \u0000 \u0000 \u0000 S\u0000 y\u0000 m\u0000 \u0000 n\u0000 \u0000 (\u0000 \u0000 R\u0000 \u0000 )\u0000 \u0000 mathbf {Sym}_n(mathbb {R})\u0000 \u0000\u0000. This allows us to establish new a priori estimates for inviscid gases flowing in the whole space \u0000\u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 d\u0000 \u0000 mathbb {R}^d\u0000 \u0000\u0000. Notably, we estimate the defect measure (Boltzman equation) or weighted spacial correlations of the velocity field (Euler system). As usual, our bounds involve only the total mass and energy of the flow.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47365257","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}
We review a series of recent results on global dynamic properties of radially symmetric self-gravitating compressible Euler flows, which naturally arise in the mathematical description of stars. We focus on the role of scaling invariances and how they interact with nonlinearities to generate imploding finite-time singularities as well as expanding star solutions, arising from smooth initial data. This review paper is based on joint works with Y. Guo, J. Jang, and M. Schrecker.
{"title":"Star dynamics: Collapse vs. expansion","authors":"Mahir Hadžić","doi":"10.1090/qam/1638","DOIUrl":"https://doi.org/10.1090/qam/1638","url":null,"abstract":"We review a series of recent results on global dynamic properties of radially symmetric self-gravitating compressible Euler flows, which naturally arise in the mathematical description of stars. We focus on the role of scaling invariances and how they interact with nonlinearities to generate imploding finite-time singularities as well as expanding star solutions, arising from smooth initial data. This review paper is based on joint works with Y. Guo, J. Jang, and M. Schrecker.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45524219","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}
P. Degond, A. Frouvelle, S. Merino-Aceituno, A. Trescases
We study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system.
{"title":"Hyperbolicity and nonconservativity of a hydrodynamic model of swarming rigid bodies","authors":"P. Degond, A. Frouvelle, S. Merino-Aceituno, A. Trescases","doi":"10.1090/qam/1651","DOIUrl":"https://doi.org/10.1090/qam/1651","url":null,"abstract":"We study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44200872","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}
We study first order differential equations with continuous almost periodic time dependence. We propose existence and global stability criteria of almost periodic solutions. Our results are specially useful in the study of one species population dynamics, such as logistic models with almost periodic parameters. Almost periodic time dependence also provides an explanation for oscillatory solutions in models of hematopoiesis disease dynamics.
{"title":"Global stability of almost periodic solutions in population dynamics","authors":"H. Díaz-Marín, O. Osuna","doi":"10.1090/qam/1636","DOIUrl":"https://doi.org/10.1090/qam/1636","url":null,"abstract":"We study first order differential equations with continuous almost periodic time dependence. We propose existence and global stability criteria of almost periodic solutions. Our results are specially useful in the study of one species population dynamics, such as logistic models with almost periodic parameters. Almost periodic time dependence also provides an explanation for oscillatory solutions in models of hematopoiesis disease dynamics.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48019206","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}
Acoustic excitation of a layered sphere by N N external and internal point sources is considered. The direct problem is solved by developing a T-Matrix method leading to the analytical determination of all the involved acoustic fields. Low-frequency far-field approximations are derived for different source distributions and scatterer’s characteristics. The behaviour of the scattering cross sections is investigated. Several inverse problems are formulated and solved analytically; thus the respective unknown quantities are recovered explicitly. These problems include localization of the sources, determination of their number, identification of the core’s type and extraction of the parameters of the scatterer’s layers.
{"title":"Excitation of a layered sphere by 𝑁 acoustic sources: Exact solutions, low-frequency approximations, and inverse problems","authors":"Andreas Kalogeropoulos, N. Tsitsas","doi":"10.1090/qam/1632","DOIUrl":"https://doi.org/10.1090/qam/1632","url":null,"abstract":"Acoustic excitation of a layered sphere by \u0000\u0000 \u0000 N\u0000 N\u0000 \u0000\u0000 external and internal point sources is considered. The direct problem is solved by developing a T-Matrix method leading to the analytical determination of all the involved acoustic fields. Low-frequency far-field approximations are derived for different source distributions and scatterer’s characteristics. The behaviour of the scattering cross sections is investigated. Several inverse problems are formulated and solved analytically; thus the respective unknown quantities are recovered explicitly. These problems include localization of the sources, determination of their number, identification of the core’s type and extraction of the parameters of the scatterer’s layers.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45667259","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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