Criterion For Uniqueness Of Solution Research Articles

Uniqueness Criterion for Solutions of Nonlocal Problems on a Finite Interval for Abstract Singular Equations

Uniqueness Criterion for Solutions of Nonlocal Problems on a Finite Interval for Abstract Singular Equations

Nonlinear quasi-static poroelasticity

We analyze a quasi-static Biot system of poroelasticity for both compressible and incompressible constituents. The main feature of this model is a nonlinear coupling of pressure and dilation through the system's permeability tensor. Such a model has been analyzed previously from the point of view of constructing weak solutions through a fully discretized approach. In this treatment, we consider simplified Dirichlet type boundary conditions in both the elastic displacement and pressure variables and give a full treatment of weak solutions. Our construction of weak solutions for the nonlinear problem is based on a priori estimates, a requisite feature in addressing the nonlinearity. We utilize a spatial semi-discretization and employ a multi-valued fixed point argument for a clear construction of weak solutions. We also provide regularity criteria for uniqueness of solutions.

Existence and multiplicity of solutions in frictional contact mechanics. Part I: A simplified criterion

The work presented hereafter deals with an important issue arising in frictional contact problems involving flexible bodies: the occurrence of more than one solution, with an emphasis on the quasi-static incremental problem in the presence of rectilinear obstacle and in two dimensions. The conditions for the existence of multiple solutions to the quasi-static incremental problem, with an intrinsic combinatorial character, are presented for several criteria. A simplified criterion is proposed that avoids the exponential character of the problem. An algorithm is proposed for the computation of all the solutions of the incremental problem and to verify the sharpness of the frictional coefficient estimates corresponding to the several criteria. The contributions may be summarized as follows: (i) new simplified (sufficient) criterion for uniqueness of solution based on the solution of an optimization problem, avoiding the exponential character of the (necessary and sufficient) complete criterion of Alart or of the (sufficient) criterion due to Andersson; the proposed criterion assumes that the onset of multiplicity is associated with a mode involving sliding in the whole contact candidate region. (ii) The use of the suggested algorithm to compute all the solutions of the quasi-static incremental problem (for a given loading) in a finite element version of Klarbring's two degree of freedom model. For some lumped mass examples, all the solutions were calculated and their dependencies on some parameters were discussed. The conditions under which a problem may have multiple solutions were also discussed for some lumped models.

Uniqueness of the solutions of the Hermite – Pade problems

New concepts are introduced in the present work. They are a quite normal index and a quite perfect system of functions. Using these concepts, the uniqueness criterion for solution of two Hermite – Pade problems is proved, the explicit determinant representations of type I and II Hermite – Padé polynomials for an arbitrary system of power series are obtained. The results obtained complement and generalize the well-known result in the theory of Hermite – Padé approximations.

A numerical method for solving linear non-autonomous systems based on linear programming

In this article we propose an approximate solution method for solving linear non-autonomous systems with an initial condition. In this method, the initial value problem is transformed into a linear programming problem to obtain an approximate solution. The existence and uniqueness criterion for solution is also proved in a linear programming manner. Finally we propose a method to find the fundamental matrix of these systems. Numerical examples are considered.

GNCA: A framework for determining transcription factor activity based on transcriptome: identifiability and numerical implementation

Network Component Analysis (NCA) is a network structure-driven framework for deducing regulatory signal dynamics. In contrast to classical approaches such as principal component analysis or independent component analysis, NCA makes use of the connectivity structure from transcriptional regulatory networks to restrict the decomposition to a unique solution. However, the existing version of NCA cannot incorporate information beyond the network topology such as information obtained from regulatory gene knockouts that constrain the dynamics of regulatory signals. The ability of incorporating such information enables a more accurate and self-consistent analysis over different experiments and extends NCA to systems that may not satisfy the identifiability criteria of NCA. In this paper, we derive a generalized form of NCA, gNCA, which significantly expands the capability of transcription network analysis by incorporating regulatory signal constraints arising from genetic knockouts. The theoretical bases including criteria for uniqueness of solution and distinguishability between networks are derived. In addition, numerical techniques for robust decomposition are discussed. gNCA is then demonstrated using an Escherichia coli wild-type strain and an isogenic arcA deletion mutant during a carbon source transition.

Uniqueness theorems for linear non-local problems for abstract differential equations

The paper deals with linear non-local problems for differential equations in Banach spaces. We prove a criterion for uniqueness of solution and obtain some corollaries and generalizations.

On unification, uniqueness and numerical analysis in plasticity

This paper addresses various aspects of a theory of multiple-mode plastic straining which unifies constitutive equations of macroscopic solids and single crystals (for both strain-hardening and strain-softening behavior). Emphasis is given to the determination of minimal criteria for uniqueness of solution to incremental boundary value problems based upon the general theory. It is established that these criteria are sufficient to assure convergence of the finite element method in such problems.

Uniqueness criteria for solutions to abstract boundary value problems

Uniqueness criteria for solutions to abstract boundary value problems