Existence and Uniqueness of Solutions in Strain Space of Elastoplastic Problems with Isotropic Hardening

1997 ◽  
Vol 07 (01) ◽  
pp. 31-48 ◽  
Author(s):  
Ivan Hlaváček ◽  
John R. Whiteman
Keyword(s):  
Existence And Uniqueness ◽  
Mixed Boundary ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Mixed Boundary Conditions ◽  
Monotone Operators ◽  
Isotropic Hardening ◽  
Uniqueness Of Solutions ◽  
Quasistatic Problem ◽  
Strain Space

The flow theory of elasto-plastic bodies with isotropic strain hardening is formulated in strain space by means of a time-dependent variational inequality. Using concepts of subdifferential and multivalued maximal monotone operators, we prove the existence and uniqueness of a solution of the quasistatic problem in ℝn, (n = 2,3), with mixed boundary conditions.

Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data

2003 ◽  
Vol 10 (3) ◽  
pp. 467-480
Author(s):  
Igor Chudinovich ◽  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Boundary Data ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boundary Integral ◽  
Integral Representations ◽  
Transverse Shear Deformation ◽  
Uniqueness Of Solutions ◽  
Nonstationary Boundary

Abstract The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.

ON THE EQUATION OF BARENBLATT–SOBOLEV

2011 ◽  
Vol 13 (05) ◽  
pp. 843-862 ◽  
Author(s):  
ADIMURTHI ◽  
NGONN SEAM ◽  
GUY VALLET
Keyword(s):  
Existence And Uniqueness ◽  
Stochastic Perturbation ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Critical Value ◽  
Sobolev Equation ◽  
Lipschitz Continuous ◽  
Sobolev Problem ◽  
Uniqueness Of The Solution

In this paper, we are interested in the following pseudoparabolic problem, known as the Barenblatt–Sobolev problem: f(∂ut) - Δu - ϵΔ∂ut = g with u(0, ⋅) = u0 where f is a non-monotone Lipschitz-continuous function, ϵ > 0 and [Formula: see text]. We show the existence of a critical value ϵ0 >0 such that: if ϵ > ϵ0, then the problem admits a unique solution; if ϵ = ϵ0, the solution is unique and it exists under an additional assumption on f; if ϵ < ϵ0, then the solution is not unique in general. Passing to the limit with ϵ to 0+, we prove the existence (and uniqueness) of the solution of the Barenblatt differential inclusion Δu + g ∈ f(∂ut) for a class of maximal monotone operators f. Next, we give an extension of the main result for a stochastic perturbation of the problem and we give some numerical illustrations of the Barenblatt and the Barenblatt–Sobolev equation.

scholarly journals Existence and uniqueness of solutions for a fractional boundary value problem on a graph

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
John Graef ◽  
Lingju Kong ◽  
Min Wang
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Point Theory ◽  
Star Graph ◽  
Fractional Boundary Value Problem ◽  
Uniqueness Of Solutions

AbstractIn this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.

Study of Some Rheological Elastoplastic Models With a Finite Number of Degrees of Freedom

1999 ◽  
Author(s):  
J. Bastien ◽  
C. H. Lamarque ◽  
M. Schatzman
Keyword(s):  
Finite Number ◽  
Existence And Uniqueness ◽  
Degrees Of Freedom ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Physical Parameters ◽  
Hysteresis Cycle ◽  
Rheological Models ◽  
Uniqueness Theory

Abstract A large number of rheological models can be covered by the existence and uniqueness theory for maximal monotone operators. Numerical simulations display hysteresis cycles when the forcing is periodic. A given shape of hysteresis cycle in an appropriate class of polygonal cycles can always be realized by adjusting the physical parameters of the rheological model.

AN EXISTENCE AND UNIQUENESS RESULT FOR AN ELASTO-PIEZOELECTRIC PROBLEM WITH DAMAGE

2009 ◽  
Vol 19 (01) ◽  
pp. 31-50 ◽  
Author(s):  
JOSÉ R. FERNÁNDEZ ◽  
KENNETH L. KUTTLER
Keyword(s):  
Existence And Uniqueness ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Coupled System ◽  
Monotone Operators ◽  
Uniqueness Result ◽  
Comparison Result ◽  
Evolutionary Equations ◽  
Micro Cracks ◽  
Piezoelectric Effects

The aim of this paper is to study the damage evolution in an elasto-piezoelectric body. The effect of the damage, due to internal tension or compression and caused by the opening and growth of micro-cracks and micro-cavities, and the piezoelectric effects are included into the model. The variational formulation leads to a coupled system of evolutionary equations. An existence and uniqueness result is then proved by using the theory of maximal monotone operators, the Schauder fixed-point theorem, and a comparison result.

scholarly journals Topological degree and application to a parabolic variational inequality problem

2001 ◽  
Vol 25 (4) ◽  
pp. 273-287 ◽  
Author(s):  
A. Addou ◽  
B. Mermri
Keyword(s):  
Variational Inequality ◽  
Topological Degree ◽  
Variational Inequality Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Parabolic Variational Inequality ◽  
Inequality Problem ◽  
Monotone Map ◽  
New Formulation

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

scholarly journals Existence and uniqueness of positive solutions for nonlinear fractional mixed problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alberto Cabada ◽  
Om Kalthoum Wanassi
Keyword(s):  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Nonlinear Part ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Exhaustive Study ◽  
The Banach Contraction Principle

Abstract This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear Riemann–Liouville fractional differential equations with mixed boundary value conditions. An exhaustive study of the sign of the related Green’s function is carried out. Under suitable assumptions on the asymptotic behavior of the nonlinear part of the equation at zero and at infinity, and by application of the fixed point theory of compact operators defined in suitable cones, it is proved that there exists at least one solution of the considered problem. Moreover, the method of lower and upper solutions is developed and the existence of solutions is deduced by a combination of both techniques. In particular cases, the Banach contraction principle is used to ensure the uniqueness of solutions.

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