Blow-up at space infinity for solutions of a system of non-autonomous semilinear heat equations

2019/04/15 by Gabriela de Jesús Cabral‐García, Cabral-García, Gabriela de Jesús, José Villa‐Morales +1
Engineering · Mathematics · #35B40 #35K20 #35K45 #35K57 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1904.07186

openalex publication_date 2019/04/15 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

In this paper we will see that the global or local existence of solutions to \dfrac∂ u₁∂ t amp; = amp; k₁ (t) Δu₁ + h₁(t) u₁^p₁₁ u₂^p₁₂,
\dfrac∂ u₂∂ t amp; = amp; k₂ (t) Δu₂ + h₂(t) u₂^p₂₂ u₁^p₂₁, depends on the initial datums and the global or local existence of solutions to \dfracdy₁dt amp; = amp; h₁(t) y₁^p₁₁(t) y₂^p₁₂(t),
\dfracdy₂dt amp; = amp; h₂(t) y₂^p₂₂(t) y₁^p₂₁(t). We also give some bounds for the maximal existence time of the partial differential system. Moreover, if such existence time is finite and min\p₁₁ + p₁₂,p₂₂+p₂₁\ > 1 then we will prove the partial differential system has solutions that blows-up at space infinite.

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