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Determination of Discontinuity Points and the Jump Magnitude of the Original Based on Its Laplace Image
AbstractThe application of the integral Laplace transform to a wide class of problems leads to a simpler equation relative to the image of the...
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Stability and Error Analysis of an Efficient Numerical Method for Convection Dominated Parabolic PDEs with Jump Discontinuity in Source Function on Modified Layer-Adapted Mesh
AbstractThis paper introduces a novel approach for analyzing efficient numerical solution of a class of singularly perturbed parabolic...
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On the Localization of Fractal Lines of Discontinuity from Noisy Data
AbstractAn ill-posed problem of localization (determining the position) of discontinuity lines of a function of two variables is considered: outside...
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A Study of New Methods for Localizing Discontinuity Lines on Extended Correctness Classes
We consider the ill-posed problem of finding the position of the discontinuity lines of a function of two variables. It is assumed that the function...
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Approximation of the Normal to the Discontinuity Lines of a Noisy Function
The work is devoted to the construction of regularizing algorithms for solving the ill-posed problem of determining the normal and the position of...
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Discontinuity Structures and Solitary Waves in Electromagnetic Hydrodynamics Associated with Linear and Nonlinear Alfvén Wave Resonances
AbstractNondissipative and weakly dissipative discontinuity structures are considered. A special numerical method for studying periodic waves is...
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Internal Transition Layer Structure in the Reaction–Diffusion Problem for the Case of a Balanced Reaction with a Weak Discontinuity
AbstractFor a singularly perturbed reaction–diffusion equation, we study the structure of the internal transition layer in the case of a balanced...
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Periodic and Solitary Waves and Nondissipative Discontinuity Structures in Electromagnetic Hydrodynamics in the Case of Wave Resonance
AbstractA numerical method is described for studying periodic waves, solitary waves, and nondissipative discontinuity structures for the equations...
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Discontinuity Detection by Null Rules for Adaptive Surface Reconstruction
We present a discontinuity detection method based on the so-called null rules, computed as a vector in the null space of certain collocation...
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Half inverse problem and interior inverse problem for the Dirac operators with discontinuity
In this paper, the half inverse problem and interior inverse problems for Dirac operators with discontinuity inside the interval (0, T ) is...
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A new Petrov–Galerkin immersed finite element method for elliptic interface problems with non-homogeneous jump conditions
In this paper, we develop a Petrov–Galerkin immersed finite element method for solving elliptic interface problems in two and three dimensions. By...
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Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth
A lower semicontinuity result and a relaxation formula for free discontinuity functionals with non-standard growth in the bulk energy are provided....
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Singular integrals and Feller semigroups with jump phenomena
This paper is devoted to the real analysis methods for the problem of construction of Markov processes with boundary conditions in probability....
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Conjugacy Problem of Strictly Monotone Maps with Only One Jump Discontinuity
The conjugacy problem is one of the important questions in iteration theory. As far as we know, for discontinuous strictly monotone maps there is no...
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Inverse problem for Hill equation with jump conditions
In the present study, the inverse nodal problem is discussed for the discontinuous periodic (or anti-periodic) Sturm–Liouville problem. Such types of...
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Generalized Riemann Problem on the Decay of a Discontinuity with Additional Conditions at the Boundary and Its Application for Constructing Computational Algorithms
We construct an approximation of the fundamental solution of a problem for a hyperbolic system of first-order linear differential equations with...
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Study of the Relations on a Stationary Flat Strong Discontinuity for a Polymeric Liquid
AbstractA flat strong discontinuity in a polymer fluid is investigated in the rheological Vinogradov−Pokrovsky model. Relationships for a strong...
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An adaptive immersed finite element method for linear parabolic interface problems with nonzero flux jump
We study an adaptive immersed finite element method for solving parabolic interface problems with nonzero flux jump in a two-dimensional convex...
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Uniqueness theorems for the impulsive Dirac operator with discontinuity
In this paper we study the impulsive Dirac operator with discontinuity and prove uniqueness theorems from introduced new supplementary data. It is...
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Direction sensitive analysis of higher order jump discontinuities along circles on the sphere
In recent years, scale-discretized directional wavelets and second-generation curvelets have been introduced on the unit sphere, yielding directional...
