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.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

scholarly journals GROUP PROPERTIES OF A ONE-DIMENSIONAL NONLINEAR POROELASTICITY EQUATION

2019 ◽  
Vol 4 (1) ◽  
pp. 149-155
Author(s):  
Kholmatzhon Imomnazarov ◽  
Ravshanbek Yusupov ◽  
Ilham Iskandarov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lie Algebra ◽  
Three Dimensional ◽  
Group Classification ◽  
Second Order ◽  
Partial Differential ◽  
One Dimensional ◽  
Preliminary Group

This paper studies a class of partial differential equations of second order , with arbitrary functions and , with the help of the group classification. The main Lie algebra of infinitely infinitesimal symmetries is three-dimensional. We use the method of preliminary group classification for obtaining the classifications of these equations for a one-dimensional extension of the main Lie algebra.

Simulation of edge-effects in electroanalytical experiments by orthogonal collocation.: Part 1. Two-dimensional collocation and theory for chronoamperometry

1982 ◽  
Vol 60 (11) ◽  
pp. 1352-1362 ◽  
Author(s):  
Bernd Speiser ◽  
Stanley Pons
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Edge Effects ◽  
Circular Disc ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Orthogonal Collocation ◽  
Partial Differential ◽  
Two Dimensional Model ◽  
Disc Electrodes

A two-dimensional model to describe edge-effects at planar circular disc electrodes has been developed. Two-dimensional orthogonal collocation is used to discretize the corresponding partial differential equations. The equations for the simulation of a chronoamperometric experiment are derived.

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