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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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Metrically Levitin–Polyak well-posed parametric set optimization problem
In this article, concepts of metrically pointwise and metrically global Levitin–Polyak (LP) well-posed parametric set optimization problems are...
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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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New Well-Posed boundary conditions for semi-classical Euclidean gravity
We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has...
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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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On Well-Posed Boundary Conditions for the Linear Non-Homogeneous Moment Equations in Half-Space
We investigate the boundary conditions that ensure the well-posedness of the linear non-homogeneous Grad moment equations in half-space. The Grad...
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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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Towards a Reliable Uncertainty Quantification in Residual Stress Measurements with Relaxation Methods: Finding Average Residual Stresses is a Well-Posed Problem
BackgroundIn a previous work, the problem of identifying residual stresses through relaxation methods was demonstrated to be mathematically...
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When is the Porous, Laminar Flow Problem with Slip Condition Well Posed? And Where Does the Solution Lie?
The aim of this article is to advance the current state of knowledge for steady, isothermal, incompressible, laminar flow within a channel featuring...
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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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Three-dimensionally nonlocal tensile nanobars incorporating surface effect: A self-consistent variational and well-posed model
A naturally discrete nanobar implies that the continuum axiom is failed, and its surface-to-volume ratio is very large. The nonlocal theory of...
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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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One-Dimensional Well-Posed Nonlocal Elasticity Models for Finite Domains
Nonlocal modeling of physical phenomena is a very long history. Researchers in scientific and engineering communities increasingly recognize that the...
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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...