scholarly journals A LARGE DEFORMATION, VISCOELASTIC, THIN ROD MODEL: DERIVATION AND ANALYSIS

2009 ◽  
Vol 19 (10) ◽  
pp. 1907-1928 ◽  
Author(s):  
J. BEYROUTHY ◽  
H. LE DRET
Keyword(s):  
Existence And Uniqueness ◽  
Finite Strain ◽  
Three Dimensional ◽  
Evolution Problem ◽  
Well Posedness ◽  
One Dimensional ◽  
Uniqueness Of The Solution ◽  
Model Derivation ◽  
Regularity Results ◽  
Strain Model

We present a Cosserat-based three-dimensional to one-dimensional reduction in the case of a thin rod, of the viscoelastic finite strain model introduced by Neff. This model is a coupled minimization/evolution problem. We prove the existence and uniqueness of the solution of the reduced minimization problem. We also show a few regularity results for this solution which allow us to establish the well-posedness of the evolution problem. Finally, the reduced model preserves observer invariance.

scholarly journals On well-posedness of a magnetization-variables model for Navier-Stokes equations with damping

2020 ◽  
Author(s):  
Abdelkerim Chaabani,
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Well Posedness ◽  
Energy Methods ◽  
Damping Term ◽  
Navier Stokes Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

This paper aims to establish existence and uniqueness results of weak and strong solution to the three-dimensional periodic magnetization-variables formulation to Navier-Stokes equations with damping term. Authors in precedent works addressed the question as to whether this model and similar ones without damping term possess a weak solution. In this vein, considering a damping term in the magnetization-variable formulation turned to be consequential as it enforces existence and uniqueness results. Energy methods, compactness methods are the main tools.

A viscoelastic thin rod model for large deformations: Numerical examples

2011 ◽  
Vol 16 (8) ◽  
pp. 887-896 ◽  
Author(s):  
Joelle Beyrouthy ◽  
Patrizio Neff
Keyword(s):  
Finite Strain ◽  
Large Deformations ◽  
Splitting Method ◽  
Evolution Problem ◽  
The Finite Element Method ◽  
Numerical Examples ◽  
Numerical Resolution ◽  
Incremental Formulation ◽  
Lagrange Elements ◽  
Strain Model

We present a Cosserat-based 3D–1D dimensional reduction for a viscoelastic finite strain model. The numerical resolution of the reduced coupled minimization/evolution problem is based on a splitting method. We start by approximating the minimization problem using the finite element method with P1 Lagrange elements. The solution of this problem is used in the time-incremental formulation of the evolution problem.

scholarly journals Existence, uniqueness and numerical solution of a fractional PDE with integral conditions

2019 ◽  
Vol 24 (3) ◽  
pp. 368-386
Author(s):  
Jesus Martín-Vaquero ◽  
Ahcene Merad
Keyword(s):  
Existence And Uniqueness ◽  
Recent Literature ◽  
Numerical Approach ◽  
Integral Conditions ◽  
Fractional Partial Differential Equation ◽  
One Dimensional ◽  
Fractional Pde ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Conditions ◽  
Hereditary Properties

This paper is devoted to the solution of one-dimensional Fractional Partial Differential Equation (FPDE) with nonlocal integral conditions. These FPDEs have been of considerable interest in the recent literature because fractional-order derivatives and integrals enable the description of the memory and hereditary properties of different substances. Existence and uniqueness of the solution of this FPDE are demonstrated. As for the numerical approach, a Galerkin method based on least squares is considered. The numerical examples illustrate the fast convergence of this technique and show the efficiency of the proposed method.

scholarly journals A one-dimensional model for elasto-capillary necking

2020 ◽  
Vol 476 (2240) ◽  
pp. 20200337
Author(s):  
Claire Lestringant ◽  
Basile Audoly
Keyword(s):  
Surface Tension ◽  
Finite Strain ◽  
Three Dimensional ◽  
One Dimensional ◽  
Localization Phenomenon ◽  
1D Model ◽  
Elastic Cylinders ◽  
Two Phases ◽  
3D Elasticity ◽  
Strain Gradient Model

We derive a nonlinear one-dimensional (1d) strain gradient model predicting the necking of soft elastic cylinders driven by surface tension, starting from three-dimensional (3d) finite-strain elasticity. It is asymptotically correct: the microscopic displacement is identified by an energy method. The 1d model can predict the bifurcations occurring in the solutions of the 3d elasticity problem when the surface tension is increased, leading to a localization phenomenon akin to phase separation. Comparisons with finite-element simulations reveal that the 1d model resolves the interface separating two phases accurately, including well into the localized regime, and that it has a vastly larger domain of validity than 1d models proposed so far.

Solvability of coupled FBSDEs with diagonally quadratic generators

2017 ◽  
Vol 17 (06) ◽  
pp. 1750043 ◽  
Author(s):  
Peng Luo ◽  
Ludovic Tangpi
Keyword(s):  
Existence And Uniqueness ◽  
Small Time ◽  
Coupled Systems ◽  
Time Interval ◽  
Well Posedness ◽  
Initial Value ◽  
Small Time Interval ◽  
Uniqueness Of The Solution ◽  
Backward Sdes

We study the well-posedness for multi-dimensional and coupled systems of forward–backward SDEs when the generator can be separated into a quadratic and a subquadratic part. We obtain the existence and uniqueness of the solution on a small time interval. Moreover, the continuity and differentiability with respect to the initial value are presented.

scholarly journals Asymptotic analysis for vanishing acceleration in a thermoviscoelastic system

2005 ◽  
Vol 2005 (2) ◽  
pp. 105-120 ◽  
Author(s):  
Elena Bonetti ◽  
Giovanna Bonfanti
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Existence And Uniqueness ◽  
Well Posedness ◽  
Boundary Values ◽  
Quasistatic Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Regularity Results

We have investigated a dynamic thermoviscoelastic system (2003), establishing existence and uniqueness results for a related initial and boundary values problem. The aim of the present paper is to study the asymptotic behavior of the solution to the above problem as the power of the acceleration forces goes to zero. In particular, well-posedness and regularity results for the limit (quasistatic) problem are recovered.

THE SCALAR KELLER–SEGEL MODEL ON NETWORKS

2013 ◽  
Vol 24 (02) ◽  
pp. 221-247 ◽  
Author(s):  
R. BORSCHE ◽  
S. GÖTTLICH ◽  
A. KLAR ◽  
P. SCHILLEN
Keyword(s):  
Network Model ◽  
Existence And Uniqueness ◽  
Computational Studies ◽  
One Dimensional ◽  
First Order ◽  
General Network ◽  
Uniqueness Of The Solution ◽  
Order Scheme ◽  
Network Topologies ◽  
The One

In this work, we extend the one-dimensional Keller–Segel model for chemotaxis to general network topologies. We define appropriate coupling conditions ensuring the conservation of mass and show the existence and uniqueness of the solution. For our computational studies, we use a positive preserving first-order scheme satisfying a network CFL condition. Finally, we numerically validate the Keller–Segel network model and present results regarding special network geometries.

scholarly journals Well-posedness and numerical approximation of tempered fractional terminal value problems

2017 ◽  
Vol 20 (5) ◽  
Author(s):  
Maria Luísa Morgado ◽  
Magda Rebelo
Keyword(s):  
Numerical Methods ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Numerical Approximation ◽  
Shooting Method ◽  
Well Posedness ◽  
Numerical Examples ◽  
Uniqueness Of The Solution ◽  
The Given ◽  
Theoretical Results

AbstractFor a class of tempered fractional terminal value problems of the Caputo type, we study the existence and uniqueness of the solution, analyze the continuous dependence on the given data, and using a shooting method we present and discuss three numerical schemes for the numerical approximation of such problems. Some numerical examples are considered in order to illustrate the theoretical results and evidence the efficiency of the numerical methods.

scholarly journals Generalized BSDE driven by a Lévy process

2006 ◽  
Vol 2006 ◽  
pp. 1-25 ◽  
Author(s):  
Mohamed El Otmani
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
Existence Of A Solution ◽  
One Dimensional ◽  
Uniqueness Of The Solution ◽  
Independent Brownian Motion ◽  
Teugels Martingales

We study the solution of one-dimensional generalized backward stochastic differential equation driven by Teugels martingales and an independent Brownian motion. We prove existence and uniqueness of the solution when the coefficient verifies some conditions of Lipschitz. If the coefficient is left continuous, increasing, and bounded, we prove the existence of a solution.

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