scholarly journals Initial Layer Analysis for a Linkage Density in Cell Adhesion Mechanisms

2018 ◽  
Vol 62 ◽  
pp. 108-122 ◽  
Author(s):  
Vuk Milisic
Keyword(s):  
Asymptotic Expansion ◽  
Singular Term ◽  
Time Derivative ◽  
Initial Layer ◽  
Limit Solution ◽  
Layer Analysis ◽  
Non Local ◽  
Asymptotic Parameter ◽  
Age Structured ◽  
Half Axis

In this paper we present a non local age structured equation involved in cell motility modeling [5, 9, 11]. It describes the evolution of a density of linkages of a point submitted to adhesion. It depends on an asymptotic parameter ɛ representing the characteristic age of linkages. Here we introduce a new initial layer term in the asymptotic expansion with respect to ɛ. This improves error estimates obtained in [5]. Moreover, we study the convergence of the time derivative of this density and show how a singular term appears when ɛ goes to zero. We show convergence, in the tight topology of measures, to the time derivative of the limit solution and a Dirac mass supported on the initial half-axis. In order to illustrate these results, numerical simulations are performed and compared to the asymptotic expansion for various values of ɛ.

Initial layer and incompressible limit for Euler–Poisson equation in nonthermal plasma

2019 ◽  
Vol 29 (09) ◽  
pp. 1733-1751
Author(s):  
Tao Luo ◽  
Shu Wang ◽  
Yan-Lin Wang
Keyword(s):  
Asymptotic Expansion ◽  
Poisson Equation ◽  
Nonthermal Plasma ◽  
Approximate Solutions ◽  
Singular Limit ◽  
Incompressible Limit ◽  
Incompressible Euler Equation ◽  
Initial Layer ◽  
Compressible Euler ◽  
Incompressible Euler

The singular limit from compressible Euler–Poisson equation in nonthermal plasma to incompressible Euler equation with an ill-prepared initial data is investigated in this paper by constructing approximate solutions of the appropriate order via an asymptotic expansion. Nonlinear asymptotic stability of initial layer approximation is established with the convergence rate.

scholarly journals Redistribution of mass from a thin interlayer between two thick dissimilar media: 1-D diffusion problem with a non-local condition

2013 ◽  
Vol 17 (3) ◽  
pp. 651-664 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Time Derivative ◽  
Diffusion Problem ◽  
Integral Approach ◽  
Classical Solutions ◽  
Basic Approach ◽  
Interface Concentration ◽  
The Media ◽  
Non Local ◽  
Thin Interlayer ◽  
Infinite Media

Diffusion problem with a specification of considering liquid redistribution from a thin interlayer between two semi-infinite media in contact is developed. The basic approach involves an integral approach defining finite depths of penetration of the diffusant into the media and fractional half-time derivative of the boundary (at the interface) concentration. The approach is straightforward and avoids cumbersome calculations based on the idea to develop entire domain (for each of the contacting bodies) solutions. The results are compared to classical solutions, when they exist.

scholarly journals Non-local porous media equations with fractional time derivative

2021 ◽  
Vol 211 ◽  
pp. 112486
Author(s):  
Esther Daus ◽  
Maria Pia Gualdani ◽  
Jingjing Xu ◽  
Nicola Zamponi ◽  
Xinyu Zhang
Keyword(s):  
Porous Media ◽  
Time Derivative ◽  
Porous Media Equations ◽  
Non Local ◽  
Fractional Time Derivative

scholarly journals Fractional thermal diffusion and the heat equation

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Francisco Gómez ◽  
Luis Morales ◽  
Mario González ◽  
Victor Alvarado ◽  
Guadalupe López
Keyword(s):  
Time Domain ◽  
Time Derivative ◽  
Space Time ◽  
Mathematical Representation ◽  
Alternative Representation ◽  
Complex Processes ◽  
Temporal Derivative ◽  
Dimensional Parameters ◽  
Non Local ◽  
Fractional Space

AbstractFractional calculus is the branch of mathematical analysis that deals with operators interpreted as derivatives and integrals of non-integer order. This mathematical representation is used in the description of non-local behaviors and anomalous complex processes. Fourier’s lawfor the conduction of heat exhibit anomalous behaviors when the order of the derivative is considered as 0 < β,ϒ ≤ 1 for the space-time domain respectively. In this paper we proposed an alternative representation of the fractional Fourier’s law equation, three cases are presented; with fractional spatial derivative, fractional temporal derivative and fractional space-time derivative (both derivatives in simultaneous form). In this analysis we introduce fractional dimensional parameters σ

Non-local modeling with asymptotic expansion homogenization of random materials

2020 ◽  
Vol 147 ◽  
pp. 103459
Author(s):  
Sami Ben Elhaj Salah ◽  
Azdine Nait-Ali ◽  
Mikael Gueguen ◽  
Carole Nadot-Martin
Keyword(s):  
Asymptotic Expansion ◽  
Local Modeling ◽  
Non Local

scholarly journals Analysis of rubella disease model with non-local and non-singular fractional derivatives

2017 ◽  
Vol 8 (1) ◽  
pp. 17-25 ◽  
Author(s):  
Ilknur Koca
Keyword(s):  
Exact Solution ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Disease Model ◽  
Time Derivative ◽  
Banach Fixed Point Theorem ◽  
Fractional Differentiation ◽  
Non Local ◽  
Time Fractional Derivative

In this paper we investigate a possible applicability of the newly established fractional differentiation in the field of epidemiology. To do this we extend the model describing the Rubella spread by replacing the time derivative with the time fractional derivative for the inclusion of memory. Detailed analysis of existence and uniqueness of exact solution is presented using the Banach fixed point theorem. Finally some numerical simulations are showed to underpin the effectiveness of the used derivative.

scholarly journals ERROR ANALYSIS OF LEGENDRE-GALERKIN SPECTRAL METHOD FOR A PARABOLIC EQUATION WITH DIRICHLET-TYPE NON-LOCAL BOUNDARY CONDITIONS

2021 ◽  
Vol 26 (2) ◽  
pp. 287-303
Author(s):  
Abdeldjalil Chattouh ◽  
Khaled Saoudi
Keyword(s):  
Parabolic Equation ◽  
Error Analysis ◽  
Boundary Conditions ◽  
Spectral Method ◽  
Time Derivative ◽  
Stability And Convergence ◽  
Local Boundary ◽  
Dirichlet Type ◽  
Non Local ◽  
Galerkin Spectral Method

An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation and the Legendre orthogonal polynomials, while the time derivative is discretized by using the symmetric Euler finite difference schema. The stability and convergence of the semi-discrete spectral approximation are rigorously set up by following a novel approach to overcome difficulties caused by the non-locality of the boundary condition. Several numerical tests are included to confirm the efficacy of the proposed method and to support the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document