scholarly journals Green’s Function of the Linearized Logarithmic Keller–Segel–Fisher/KPP System

2018 ◽  
Vol 23 (4) ◽  
pp. 56 ◽  
Author(s):  
Jean Rugamba ◽  
Yanni Zeng
Keyword(s):  
Nonlinear System ◽  
Green’S Function ◽  
Green's Function ◽  
Linear Problem ◽  
Logarithmic Singularity ◽  
Complete Solution ◽  
Logistic Growth ◽  
Chemotaxis Model ◽  
Logarithmic Sensitivity ◽  
Shed Light

We consider a Keller–Segel type chemotaxis model with logarithmic sensitivity and logistic growth. The logarithmic singularity in the system is removed via the inverse Hopf–Cole transformation. We then linearize the system around a constant equilibrium state, and obtain a detailed, pointwise description of the Green’s function. The result provides a complete solution picture for the linear problem. It also helps to shed light on small solutions of the nonlinear system.

scholarly journals Recent results for the logarithmic Keller-Segel-Fisher/KPP System

2019 ◽  
Vol 38 (7) ◽  
pp. 37-48
Author(s):  
Yanni Zeng ◽  
Kun Zhao
Keyword(s):  
Ground State ◽  
Decay Rates ◽  
Optimal Time ◽  
Logistic Growth ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Chemotaxis Model ◽  
Time Decay Rates ◽  
Long Time ◽  
Logarithmic Sensitivity

We consider a Keller-Segel type chemotaxis model with logarithmic sensitivity and logistic growth. It is a 2 by 2 system describing the interaction of cells and a chemical signal. We study Cauchy problem with finite initial data, i.e., without the commonly used smallness assumption on  initial perturbations around a constant ground state. We survey a sequence of recent results by the authors on  the existence of global-in-time solution,  long-time behavior, vanishing coefficient limit and optimal time decay rates of the solution.

The Elastodynamic Green’s Function for a Torsional Ring Source

1998 ◽  
Vol 65 (3) ◽  
pp. 566-568 ◽  
Author(s):  
Yichi Lu
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Legendre Function ◽  
Logarithmic Singularity ◽  
Hankel Transform ◽  
Linear Elastic ◽  
Half Degree ◽  
Homogeneous Linear ◽  
Ring Source

The elastodynamic Green’s fimction for a torsional ring source in a homogeneous, linear elastic medium is derived using the Fourier-Hankel transform. The Green’s function is found to possess the same logarithmic singularity as the Legendre function of half-degree of the second kind.

GREEN'S FUNCTION MATCHING METHOD FOR REALISTIC CALCULATIONS OF INTERFACES

1985 ◽  
Vol 46 (C4) ◽  
pp. C4-321-C4-329 ◽  
Author(s):  
E. Molinari ◽  
G. B. Bachelet ◽  
M. Altarelli
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Matching Method

THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT

2014 ◽  
Vol 17 (N/A) ◽  
pp. 89-145 ◽  
Author(s):  
Sridhar Sadasivam ◽  
Yuhang Che ◽  
Zhen Huang ◽  
Liang Chen ◽  
Satish Kumar ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Phonon Transport ◽  
Green’S Function Method
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