Weak solvability of a fractional Voigt viscoelasticity model

The existence of a weak solution of a boundary value problem for a fractional Voigt viscoelasticity model is proved. The proof relies on an approximation of the original boundary value problem by regularized ones and recent results concerning the solvability of Cauchy problems for systems of ordinary differential equations in the class of regular Lagrangian flows.     

On the weak solvability of the problem of viscoelasticity with memory

The existence of a weak solution is proved for a certain Oldroyd model of motion of a viscoelastic medium that allows for the memory of the system. The proof uses the theory of regular Lagrange flows and a topological approximation method that reduces the posed problem to an operator equation, its ε-regularization in smoother spaces, the use of a priori estimates and a topological degree for the proof of the solvability of the ε-regularized equations, and the passage to the limit as ε → 0.     

New approach to the solvability of generalized Navier-Stokes equations

We propose a new approach to prove the existence of weak solutions to generalized (or modified) Navier-Stokes equations. We also consider systems presently well known from the theory of non-Newtonian electrorheological fluids.     

Weak solvability of antiplane frictional contact problems for elastic cylinders

We study a mathematical model which describes the antiplane shear deformations of a cylinder in frictional contact with a rigid foundation. The process is static, the material behavior is described with a linearly elastic constitutive law and friction is modeled with a general slip dependent subdifferential boundary condition. We derive a variational formulation of the model which is in a form of a hemivariational inequality for the displacement field. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proofs are based on abstract results for operator inclusions in Banach spaces. Finally, we present concrete examples of friction laws for which our results are valid.     

Weak and strong solvability of parabolic variational inequalities in Banach spaces

We consider parabolic variational inequalities having the strong formulation

On the solvability of generalized Stokes equations in the spaces of periodic functions

The paper is concerned with the solvability theory of the generalized Stokes equations arising in the study of the motion of non-newtonian fluids.

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Sunto Il lavoro si occupa della teoria dell’esistenza di soluzioni per le equazioni generalizzate di Stokes motivate dallo studio del moto di fluidi non newtoniani.

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Dedicated to the memory of Professor S. N. Kruzhkov     

Weak continuity on generalized topological spaces

We introduce the notions of weak (g, g′)-continuity and weak (ψ, ψ′)-continuity on GTS’s and GNS’s, respectively, and investigate characterizations for such functions and relationships between weak (g, g′)-continuity and weak (ψ, ψ′)-continuity.     

On the solvability of the Tricomi problem with a generalized Frankl transmission condition

We study the solvability of the Tricomi problem for the Lavrent’ev-Bitsadze equation with mixed boundary conditions in the elliptic part of the domain. On the type change line of the equation, the solution gradient is subjected to a condition that is usually referred to as the generalized Frankl transmission condition. We show that the inhomogeneous Tricomi problem either has a unique solution or is conditionally solvable and the homogeneous problem has only the trivial solution. We write out an integral representation of the solution of this problem.     

Weak convergence for generalized semi-Markov processes

Generalized semi-Markov schemes were introduced by Matthes in 1962 under the designation ‘Bedienungsschemata’ (service schemes). They include a large variety of familiar stochastic models. It is shown in this paper that under appropriate regularity conditions the associated stochastic process describing the state at timet,t≥0, and the stationary distribution are continuous functions of the life-times of the active components. The supplementary-variable Markov process is shown to be the limit process of a sequence of discrete-state-process obtained through approximating the life-time distributions by mixtures of Erlang distributions and measuring ages and residual life-times in phases. This approach supplements the phase method.     

Weak sharp solutions for generalized variational inequalities

We consider weak sharp solutions for the generalized variational inequality problem, in which the underlying mapping is set-valued, and not necessarily monotone. We extend the concept of weak sharpness to this more general framework, and establish some of its characterizations. We establish connections between weak sharpness and (1) gap functions for variational inequalities, and (2) global error bound. When the solution set is weak sharp, we prove finite convergence of the sequence generated by an arbitrary algorithm, for the monotone set-valued case, as well as for the case in which the underlying set-valued map is either Lipschitz continuous in the set-valued sense, for infinite dimensional spaces, or inner-semicontinuous when the space is finite dimensional.     

A study of the solvability of the generalized equation of filtration of an inhomogeneous fluid

We study the existence of solutions of the generalized equation of filtration of an inhomogeneous fluid and prove that they are unique. We study the smoothness properties of the solutions when the right-hand sides of the equation belong to various spaces.This work is carried out using the machinery of rigged Hilbert spaces and energy inequalities.Translated fromVychislitel'naya i Prikladnaya Matematika, Issue 71, 1990, pp. 77–84.     

Weak separation axioms in generalized topological spaces

We study a unified approach of weak separation axioms in generalized topological spaces.     

Weak descartes systems in generalized spline spaces

A class of generalized spline spaces is introduced for which a basis of functions with local support is constructed by using a recursion relation. It is shown that this basis forms a weak Descartes system. Moreover, an interpolation property is given.