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Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunctions
In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the...
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Angular Scattering Function Estimation Using Deep Neural Networks
In this chapter, we study the problem of angular scattering function (ASF) estimation for a massive multiple-input multiple-output (MIMO) system. In...
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On the Local Solvability and Stability for the Inverse Spectral Problem of the Generalized Dirichlet—Regge Problem
For the generalized Dirichlet—Regge problem with complex coefficients, we prove the local solvability and stability for the inverse spectral problem,...
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An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane
An efficient direct solver for solving the Lippmann–Schwinger integral equation modeling acoustic scattering in the plane is presented. For a problem...
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An inverse boundary value problem for isotropic nonautonomous heat flows
We study an inverse boundary value problem on the determination of principal order coefficients in isotropic nonautonomous heat flows stated as...
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Conforming element method and shifted-inverse two-grid dicretization for the fourth-order Steklov eigenvalue problem
The fourth-order Steklov eigenvalue problem is essential in analyzing the supported plate and the deformation of the linear elastic hinge phenomenon....
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Inverse Spectral Problem for Integro-Differential Sturm–Liouville Operators with Discontinuity Conditions
We consider the Sturm–Liouville operator perturbed by a convolution integral operator on a finite interval with Dirichlet boundary conditions and...
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Free boundary methods and non-scattering phenomena
We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We...
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Scattering of plane SH waves by a concentric semi-cylindrical discontinuity and canyon
The discontinuity of the medium and the irregularity of the ground significantly affect the propagation of seismic waves. However, the comprehensive...
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Mathematical Scattering Theory in Quantum and Acoustic Waveguides
We consider a waveguide that occupies a domain G with several cylindrical ends and is descried by the nonstationary equation
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Acoustic Scattering in the Time Domain
In this chapter we turn to the main motivation for the book: the numerical modelling of transient acoustic wave propagation. After giving an...
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A fast solver for elastic scattering from axisymmetric objects by boundary integral equations
Fast and high-order accurate algorithms for three-dimensional elastic scattering are of great importance when modeling physical phenomena in...
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Scattering for the Mass-Critical Nonlinear Klein–Gordon Equations in Three and Higher Dimensions
In this paper we consider the mass-critical nonlinear Klein–Gordon equations in three and higher dimensions. We prove the dichotomy between...
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A new improved teaching–learning-based optimization (ITLBO) algorithm for solving nonlinear inverse partial differential equation problems
Teaching–learning-based optimization (TLBO) algorithm is a novel population-oriented meta-heuristic algorithm. In this paper, we introduce an...
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Direct Problem of Scattering Theory for a Dirac System of Differential Equations on the Half-Line in the Case of Finite Density
AbstractIn this paper, we study the direct scattering problem on the half-line for the Dirac system of differential equations in the case of finite...
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Inverse heat conduction problem with a nonlinear source term by a local strong form of meshless technique based on radial point interpolation method
This study is devoted to find the numerical solution of the surface heat flux history and temperature distribution in a non linear source term...
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The Derivative Nonlinear Schrödinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms and N-Double-Pole Solutions
In this paper, we report a rigorous theory of the inverse scattering transforms (ISTs) for the derivative nonlinear Schrödinger (DNLS) equation with...
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Gentle Algebras Arising from Surfaces with Orbifold Points of Order 3, Part I: Scattering Diagrams
To each triangulation of any surface with marked points on the boundary and orbifold points of order three, we associate a quiver (with loops) with...
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An Introduction to the Mathematical Theory of Inverse Problems
This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system...