The solution of unbounded Helmholtz problems is the subject of substantial research. If these problems are to be solved using a domain-based discretisation technique like the finite element method (FEM), the computational domain has to be truncated to a bounded region. The unbounded nature of the problem exterior to this truncation is simulated by an appropriate condition on the truncation. A c...

In this paper we investigate Multi-Objective Integer Linear Programming (MOILP) problems with unbounded feasible region and introduce recession direction for MOILP problems. Then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of MOILP problems. Finally we present some examples with unbounded feasible region and fi...

We study existence of minimisers to the least gradient problem on a strictly convex domain in two settings. On bounded domain, we allow boundary data be discontinuous and prove terms Hausdorff measure discontinuity set. Later, unbounded, their properties regularity shape domain.

In this paper we consider the numerical simulations of the incompressible materials on an unbounded domain in <2. A series of artificial boundary conditions at a circular artificial boundary for solving incompressible materials on an unbounded domain is given. Then the original problem is reduced to a problem on a bounded domain, which be solved numerically by a mixed finite element method. The...

In this work, a new mathematical model of thermoelasticity theory has been considered in the context of a new consideration of heat conduction with fractional order theory. A functionally graded isotropic unbounded medium is considered subjected to a periodically varying heat source in the context of space-time non-local generalization of three-phase-lag thermoelastic model and Green-Naghdi mod...

Definition 1. Let f and g be functions in ω. We say that f is dominated by g iff there is some natural number n such that f ≤n g, i.e. (∀i ≥ n)(f(i) ≤ g(i)). Then <∗= ∪ ≤n is called the bounding relation on ω. If F is a family of functions in ω we say that F is dominated by the function g, and denote it by F <∗ g iff (∀f ∈ F)(f <∗ g). We say that F is unbounded (also not dominated) iff there is...