Existence and density conservation using a non-conservative approximation for Safronov-Dubovski aggregation equation

2022/11/14 by Sonali Kaushik, Kaushik, Sonali, Kumar, Rajesh
Mathematics · Medicine · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.2211.07310

openalex publication_date 2022/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper deals with the global existence and density conservation for the Safronov-Dubovski equation for three different coefficients ϕ such that ϕ_i,j ≤ \frac(i+j)min\i,j\, ϕ_i,j ≤ (i+j) and ϕ_i,j ≤ (1+i+j)^α ∀ i,j ∈ ℕ, α∈ [0,1]. The non-conservative approximation is applied to study the problem and results such as Helly's selection theorem and the refined version of the De la Vallée-Poussin theorem are implemented to establish the existence of each case of the kernel. The article also focuses on the conditions for the conservation of mass per unit volume for such an equation.

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