scholarly journals Dynamics of one-fold symmetric patches for the aggregation equation and collapse to singular measure

2019 ◽  
Vol 12 (8) ◽  
pp. 2003-2065
Author(s):  
Taoufik Hmidi ◽  
Dong Li
Keyword(s):  
Singular Measure ◽  
Aggregation Equation

scholarly journals Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation

2018 ◽  
Vol 52 (2) ◽  
pp. 567-593 ◽  
Author(s):  
Li Chen ◽  
Simone Göttlich ◽  
Stephan Knapp
Keyword(s):  
Particle System ◽  
Rigorous Derivation ◽  
Uniform Estimates ◽  
Estimates Of Solutions ◽  
Delta Potential ◽  
Intermediate Particle ◽  
Stochastic Particle System ◽  
Aggregation Equation ◽  
Discretization Schemes ◽  
Theoretical Results

In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a stochastic particle system while introducing an intermediate particle system with smooth interaction potential. The theoretical results are compared to numerical simulations relying on suitable discretization schemes for the microscopic and macroscopic level. In particular, the regime switch where the analytic theory fails is numerically analyzed very carefully and allows for a better understanding of the equation.

scholarly journals Numerical solution for an aggregation equation with degenerate diffusion

2020 ◽  
Vol 377 ◽  
pp. 125145
Author(s):  
Roberto Carlos Cabrales ◽  
Juan Vicente Gutiérrez-Santacreu ◽  
José Rafael Rodríguez-Galván
Keyword(s):  
Numerical Solution ◽  
Degenerate Diffusion ◽  
Aggregation Equation

scholarly journals Income elasticity of demand within individual consumer groups and the level of income elasticity of the entire market demand 

2012 ◽  
Vol 52 (No. 9) ◽  
pp. 412-417
Author(s):  
P. Syrovátka
Keyword(s):  
Consumer Behaviour ◽  
Income Elasticity ◽  
Meat Products ◽  
Market Demand ◽  
Demand Functions ◽  
Elasticity Of Demand ◽  
Income Elasticities ◽  
Aggregation Equation ◽  
Application Potential ◽  
Income Elasticity Of Demand

The paper is focused on the derivation of the mathematical relationship among the income-elasticity level of the entire market demand and the income-elasticity values of the demand functions of the consumers’ groups buying on the defined market. The determination of the mathematical term was based on the linearity of the relevant demand functions. Under the linearity assumption, the income elasticity coefficient of the entire market demand equals the weighted sum of the income-demand elasticities of the differentiated consumer groups buying on the given market. The weights in the aggregation formula are defined as the related demand shares, i.e. as the proportions of the groups’ demands to the entire market demand. The derived aggregation equation is quite held if no demand interactions (e.g. the snob or fashion effect) are recorded among differentiated consumers’ groups. The derived formula was examined by using empirical data about the consumer behaviour of Czech households in the market of meat and meat products (Czech Statistical Office). However, the application potential of the achieved term for the income-elasticity aggregations is much broader within the consumer-behaviour analysis. In addition to the subject aggregations of the demand functions, we can also apply the derived formula for the analysis and estimations of the income elasticities within the demand-object aggregations, i.e. the multistage analysis of the income elasticity of consumer demand. Another possibility of the use of the aggregation equation is for the evaluations and estimations of the income elasticity of the region-demand functions in relation to the subregions’ demands or reversely.

scholarly journals An aggregation equation with a nonlocal flux

2014 ◽  
Vol 108 ◽  
pp. 260-274 ◽  
Author(s):  
Rafael Granero-Belinchón ◽  
Rafael Orive-Illera
Keyword(s):  
Aggregation Equation
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