Fixed Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces
Abstract In this paper, we extend the concept of b-metric spaces to the vectorial case, where the distance is vector…
(preprint)
On equilibrium in control problems with applications to evolution systems
Abstract In this paper we examine a mutual control problem for systems of two abstract evolution equations subject to a…
Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: Simulation results
Abstract This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in…
A Mutual Control Problem for Semilinear Systems via Fixed Point Approach
Abstract In this paper, we introduce and discuss the concept of a mutual control problem. Our analysis relies on a…
Optimal finite element approximation of unique continuation
Abstract We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is…
Computational orders of convergence of iterative methods for Richards’ equation
Abstract Numerical solutions for flows in partially saturated porous media pose challenges related to the non-linearity and elliptic-parabolic degeneracy of…
Role of partial functionals in the study of variational systems
Abstract Applying techniques originally developed for systems lacking a variational structure, we establish conditions for the existence of solutions in…
On high-order conforming finite element methods for ill-posed Helmholtz problems
Abstract We consider the numerical approximation of the linear ill-posed problem of unique continuation for the Helmholtz equation. We first…
Tikhonov regularization of a perturbed heavy ball system with vanishing damping
AbstractThis paper deals with aa perturbed heavy ball system with vanishing damping that contains a Tikhonov regularization term, in connection…
Accurate spectral collocation solutions to some Bratu’s type boundary value problems
AbstractWe solve by Chebyshev spectral collocation some genuinely nonlinear Liouville-Bratu-Gelfand type, 1D and a 2D boundary value problems. The problems…