Regularization and Well-Posedness by Noise for Ordinary and Partial Differential Equations

2018 ◽  
pp. 43-67 ◽  
Author(s):  
Benjamin Gess
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Well Posedness ◽  
Partial Differential

scholarly journals MATHEMATICAL ANALYSIS OF A ONE-DIMENSIONAL MODEL FOR AN AGING FLUID

2013 ◽  
Vol 23 (09) ◽  
pp. 1561-1602
Author(s):  
DAVID BENOIT ◽  
LINGBING HE ◽  
CLAUDE LE BRIS ◽  
TONY LELIÈVRE
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mathematical Analysis ◽  
Newtonian Fluids ◽  
Well Posedness ◽  
Dimensional Model ◽  
Partial Differential ◽  
One Dimensional ◽  
Longtime Behavior

We study mathematically a system of partial differential equations arising in the modeling of an aging fluid, a particular class of non-Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and investigate the longtime behavior of the solutions.

DRAPING WOVEN SHEETS

2021 ◽  
pp. 1-31
Author(s):  
P. D. HOWELL ◽  
H. OCKENDON ◽  
J. R. OCKENDON
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Carbon Fibre ◽  
Continuum Limit ◽  
Woven Fabric ◽  
Hyperbolic Partial Differential Equations ◽  
Well Posedness ◽  
Partial Differential ◽  
Rigid Rods ◽  
The Continuum

Abstract Motivated by the manufacture of carbon fibre components, this paper considers the smooth draping of loosely woven fabric over rigid obstacles, both smooth and nonsmooth. The draped fabric is modelled as the continuum limit of a Chebyshev net of two families of short rigid rods that are freely pivoted at their joints. This approach results in a system of nonlinear hyperbolic partial differential equations whose characteristics are the fibres in the fabric. The analysis of this system gives useful information about the drapability of obstacles of many shapes and also poses interesting theoretical questions concerning well-posedness, smoothness and computability of the solutions.

Draping woven sheets

2021 ◽  
Vol 62 ◽  
pp. 355-385
Author(s):  
P. D. Howell ◽  
H. Ockendon ◽  
J. R. Ockendon
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Carbon Fibre ◽  
Continuum Limit ◽  
Woven Fabric ◽  
Hyperbolic Partial Differential Equations ◽  
Well Posedness ◽  
Partial Differential ◽  
Rigid Rods ◽  
The Continuum

Motivated by the manufacture of carbon fibre components, this paper considers the smooth draping of loosely woven fabric over rigid obstacles, both smooth and nonsmooth. The draped fabric is modelled as the continuum limit of a Chebyshev net of two families of short rigid rods that are freely pivoted at their joints. This approach results in a system of nonlinear hyperbolic partial differential equations whose characteristics are the fibres in the fabric. The analysis of this system gives useful information about the drapability of obstacles of many shapes and also poses interesting theoretical questions concerning well-posedness, smoothness and computability of the solutions. doi:10.1017/S144618112000019X

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