Global existence in the critical and subcritical cases to the Fisher-KPP model with nonlocal nonlinear reaction

2019/10/20 by Shen Bian, Bian, Shen
Mathematics · Medicine · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1910.08905

openalex publication_date 2019/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Cauchy problem considered in this paper is the following \ u_t=Δu+u^α(M₀- ∫_ℝⁿ u(x,t)dx), · amp; x ∈ ℝⁿ, t · gt;0, u(x,0)=U₀(x)≥ 0, · amp; x ∈ ℝⁿ. . where M₀>0, α>1, n ≥ 3. When the coefficient M₀-∫_ℝⁿ u(x,t) dx remains positive, \ernkpp0 is analogous to \ u_t=Δu+u^α, · amp; x ∈ ℝⁿ, t · gt;0, u(x,0)=U₀(x)≥ 0, · amp; x ∈ ℝⁿ. . It is well known that when 1

Citations

• A nonlocal reaction diffusion equation and its relation with Fujita exponent
• Blowing-up of solution for a nonlocal reaction-diffusion problem in combustion theory
• Modeling the Effects of Space Structure and Combination Therapies on Phenotypic Heterogeneity and Drug Resistance in Solid Tumors

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