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On the Solvability of Initial and Boundary Value Problems for Abstract Functional-Differential Euler–Poisson–Darboux Equations
AbstractIn a Banach space, we consider the Cauchy problem and the Dirichlet and Neumann boundary value problems for a functional-differential...
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On Contact Problems with a Deformable Punch and Variable Rheology
AbstractThe paper presents for the first time one of the methods for studying and solving contact problems with a deformed stamp for those cases when...
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Random block-coordinate methods for inconsistent convex optimisation problems
We develop a novel randomised block-coordinate primal-dual algorithm for a class of non-smooth ill-posed convex programs. Lying midway between the...
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Scalar, Multidimensional Variational Problems
Once we have established a solid functional-analytical foundation, we are ready to tackle multidimensional variational problems in which we pretend...
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A Joint Logic of Problems and Propositions
AbstractIn a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper On the interpretation of intuitionistic logic ...
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Novel Multi-level Projected Iteration to Solve Inverse Problems with Nearly Optimal Accuracy
In this paper, we introduce a novel nonlinear projected iterative method to solve the ill-posed inverse problems in Banach spaces. This method is...
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On some variational inequality-constrained control problems
In this paper, by considering some properties associated with scalar functionals of multiple-integral type, we study the well-posedness and...
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Method of Inverse Problems for Thermal Diagnostics of Thermoelastic Structures
The application of inverse problems to thermal diagnostics of homogeneous structures is outlined, variational formulations of the problems under...
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Solutions with Power Type or Exponential Singularity for (3+1)-D Protter-Morawetz Problems
Transonic flows in fluid dynamics are modelled by mixed-type equations on the plane. On the other hand, M. H. Protter proposed multi-dimensional...
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Stiff Problems
In some cases, the choice of the numerical method to be used is driven by some features of the problems itself, which have to properly be taken into...
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Regularising Inverse Problems with Generative Machine Learning Models
Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this survey paper, we consider...
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Boundary Value Problems for Quasi-Hyperbolic Equations with Degeneration
AbstractThe paper deals with the solvability analysis of boundary value problems for degenerate higher-order quasi-hyperbolic equations. The...
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Minimization and Optimal Control Problems
We start this chapter with the well-posedness of a class of minimization problems. Thereby, under specific assumptions, we deduce their weak and...
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Problems on Small Motions of Systems of Two Viscoelastic Fluids in Fixed Vessels
In this paper, we study the problem on small motions of two Oldroyd viscoelastic incompressible fluids contained in a fixed vessel. By means of the...
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Rectangular eigenvalue problems
Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are...
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Differential-Algebraic Boundary-Value Problems with Impulsive Action
We establish constructive conditions of solvability of linear differential-algebraic boundary-value problems with impulsive action and propose a...
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The solvability of inhomogeneous boundary-value problems in Sobolev spaces
The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary...
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Tikhonov-regularized weighted total least squares formulation with applications to geodetic problems
This contribution presents the Tikhonov regularized weighted total least squares (TRWTLS) solution in an errors-in-variables (EIV) model. The...
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Neurobehavioral problems at age 2 years in children with prenatal opioid exposure
ObjectiveTo evaluate factors associated with borderline/clinical range Child Behavior Checklist (CBCL) scores in opioid-exposed children.
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Convergent Regularization in Inverse Problems and Linear Plug-and-Play Denoisers
Regularization is necessary when solving inverse problems to ensure the well-posedness of the solution map. Additionally, it is desired that the...
