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Investigation of Finite-Difference Analogue of the Integral Geometry Problem with a Weight Function
Finite—difference analogue of the two-dimensional problem of integral geometry with a weight function are studied.Bakanov, Galitdin B. The stability...
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Basic Results of Integral Geometry
The results in this chapter are of a geometric nature, and they emanate from the basic concept of motion-invariant measure associated with a mobile...
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Inverse coefficient problem for a fractional wave equation with time-nonlocal and integral overdetermination conditions
This work considers an initial-boundary value and an inverse coefficient problem for a fractional wave equation. Firstly, we construct Green’s...
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A Stability Estimate for a Solution to an Inverse Problem for a Nonlinear Hyperbolic Equation
We consider a hyperbolic equation with variable leading part and nonlinearity in the lower-order term. The coefficients of the equation are smooth...
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Inverse Problem for a Nonlinear Wave Equation
AbstractWe consider the inverse problem of determining the coefficient of the nonlinear term in an equation whose main part is the wave operator....
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Oscillatory integral operators with homogeneous phase functions
Oscillatory integral operators with 1-homogeneous phase functions satisfying a convexity condition are considered. For these we show the L p – L p -estimat...
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High-Frequency Estimates on Boundary Integral Operators for the Helmholtz Exterior Neumann Problem
We study a commonly-used second-kind boundary-integral equation for solving the Helmholtz exterior Neumann problem at high frequency, where, writing
... 
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Radial integral boundary element method for simulating phase change problem with mushy zone
A radial integral boundary element method (BEM) is used to simulate the phase change problem with a mushy zone in this paper. Three phases, including...
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Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets
AbstractSome questions concerning the inversion of the classical and generalized integral Radon transforms are discussed. The main issue is to...
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Galerkin-based quasi-smooth manifold element (QSME) method for anisotropic heat conduction problems in composites with complex geometry
The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance...
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Stability in Inverse Problem of Determining Two Parameters for the Moore-Gibson-Thompson Equation with Memory Terms
In this paper, the authors consider the inverse problem for the Moore-Gibson-Thompson equation with a memory term and variable diffusivity, which...
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Numerical solutions of a class of linear and nonlinear Volterra integral equations of the third kind using collocation method based on radial basis functions
In this paper, we use a method based on radial basis functions and the collocation method for the numerical solution of a class of Volterra integral...
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Integral Representations and Integral Identities
Working in the complex plane, in §1.1 we prove versions of the classical Cauchy-Pompeiu integral representation formula, Morera’s Theorem, the...
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Compact Approximation of a Two-Dimensional Boundary Value Problem for Elliptic Equations of the Second Order with a Discontinuous Coefficient
AbstractFor an elliptic equation of the second order with variable discontinuous coefficients and the right side, a scheme of the fourth order of...
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Dirac Geometry I: Commutative Algebra
The purpose of this paper and its sequel is to develop the geometry built from the commutative algebras that naturally appear as the homology of...
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FMM-Accelerated Solvers for the Laplace–Beltrami Problem on Complex Surfaces in Three Dimensions
The Laplace–Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface...
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Well-posedness of nonlinear flows on manifolds of bounded geometry
We present straightforward conditions which ensure that a strongly elliptic linear operator L generates an analytic semigroup on Hölder spaces on an...
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Inverse Problem of Pure Bending of a Beam under Creep Conditions
AbstractWe propose an algorithm for solving the inverse problem of forming structural members under creep conditions using the Nelder–Mead...
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A Stability Estimate in the Source Problem for the Radiative Transfer Equation
AbstractA stability estimate for the solution of a source problem for the stationary radiative transfer equation is given. It is supposed that the...
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On the Smoothness of a Function at the Convergence Point of Its Spectral Expansion Associated with B-Elliptic Operators
AbstractIn this paper, the necessary conditions for summability of spectral expansions in eigenfunctions of the Bessel type singular elliptic...