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Well-Posed Nonlinear Problems A Study of Mathematical Models of Contact
This monograph presents an original method to unify the mathematical theories of well-posed problems and contact mechanics. The author uses a new...
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Well-Posedness of Boundary-Value Problems for Conditionally Well-Posed Integro-Differential Equations and Polynomial Approximations of Their Solutions
The this paper, we introduce a pair of Sobolev spaces with special Jacobi–Gegenbauer weights, in which the general boundary-value problem for a class...
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Quasi-Solution Method and Global Minimization of the Residual Functional in Conditionally Well-Posed Inverse Problems
AbstractA class of conditionally well-posed problems characterized by a Hölder conditional stability estimate on a convex compact set in a Hilbert...
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A Well-Posed Logarithmic Counterpart of an Ill-Posed Cauchy Problem
In this short paper, we study a well-posed logarithmic counterpart of an ill-posed Cauchy problem associated with an abstract evolution equation of...
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Well-posed fixed point results and data dependence problems in controlled metric spaces
The present research is aimed to analyze the existence of strict fixed points (SFPs) and fixed points of multivalued generalized contractions on the...
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Well-Posed Solvability of Volterra Integro-Differential Equations in Hilbert Spaces
AbstractWe study the well-posed solvability of initial value problems for Volterra integro-differential equations in a Hilbert space with kernels of...
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On the global minimization of discretized residual functionals of conditionally well-posed inverse problems
We consider a class of conditionally well-posed inverse problems characterized by a Hölder estimate of conditional stability on a convex compact in a...
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On Well-posed Variational Problems Involving Multidimensional Integral Functionals
In this chapter, based on the notions of monotonicity, pseudomonotonicity, and hemicontinuity associated with the considered path-independent...
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Solving a well-posed fractional initial value problem by a complex approach
Nonlinear fractional differential equations have been intensely studied using fixed point theorems on various different function spaces. Here we...
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Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem
In this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q -differential equations, is...
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Three old problems from the Polish school of mathematics
This note deals with three problems posed in the 1930s by two prominent members of the Polish school of mathematics. The first problem is known as...
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Well-posed results for nonlocal biparabolic equation with linear and nonlinear source terms
In this paper, we consider the biparabolic problem under nonlocal conditions with both linear and nonlinear source terms. We derive the regularity...
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Harmonic Measures and Numerical Computation of Cauchy Problems for Laplace Equations
It is well known that the Cauchy problem for Laplace equations is an ill-posed problem in Hadamard’s sense. Small deviations in Cauchy data may lead...
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Initial–Boundary Value Problems for Homogeneous Parabolic Systems in a Semibounded Plane Domain and Complementarity Condition
AbstractWe consider initial–boundary value problems for homogeneous parabolic systems with coefficients satisfying the double Dini condition with...
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Constrained Linear-Quadratic Optimization Problems with Parameter-Dependent Entries
The paper provides strong convergence of solutions to a sequence of linear-quadratic (LQ) optimization problems defined in an abstract functional...
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Solving Ill-Posed Problems of the Theory of Elasticity Using High-Performance Computing Systems
A method for the efficient analysis and solution of conditionally well-posed problems with a unique solution in the subspace is proposed. The use of...
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Numerical methods for the forward and backward problems of a time-space fractional diffusion equation
In this paper, we consider the numerical methods for both the forward and backward problems of a time-space fractional diffusion equation. For the...
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A Broken FEEC Framework for Electromagnetic Problems on Mapped Multipatch Domains
We present a framework for the structure-preserving approximation of partial differential equations on mapped multipatch domains, extending the...
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Asymptotics of the Spectrum of Variational Problems Arising in the Theory of Fluid Oscillations
This work is a survey of results on the spectral asymptotics of variational problems arising in the theory of small oscillations of a fluid in a...
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A Weighted Hybridizable Discontinuous Galerkin Method for Drift-Diffusion Problems
In this work, we propose a weighted hybridizable discontinuous Galerkin method (W-HDG) for drift-diffusion problems. By using specific exponential...
