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Protection Zones in Periodic-Parabolic Problems
Advanced Nonlinear Studies ( IF 1.8 ) Pub Date : 2020-05-01 , DOI: 10.1515/ans-2020-2084
Julián López-Gómez 1
Affiliation  

Abstract This paper characterizes whether or not Σ ∞ ≡ lim λ ↑ ∞ ⁡ σ ⁢ [ 𝒫 + λ ⁢ m ⁢ ( x , t ) , 𝔅 , Q T ] \Sigma_{\infty}\equiv\lim_{\lambda\uparrow\infty}\sigma[\mathcal{P}+\lambda m(% x,t),\mathfrak{B},Q_{T}] is finite, where m ⪈ 0 {m\gneq 0} is T-periodic and σ ⁢ [ 𝒫 + λ ⁢ m ⁢ ( x , t ) , 𝔅 , Q T ] {\sigma[\mathcal{P}+\lambda m(x,t),\mathfrak{B},Q_{T}]} stands for the principal eigenvalue of the parabolic operator 𝒫 + λ ⁢ m ⁢ ( x , t ) {\mathcal{P}+\lambda m(x,t)} in Q T ≡ Ω × [ 0 , T ] {Q_{T}\equiv\Omega\times[0,T]} subject to a general boundary operator of mixed type, 𝔅 {\mathfrak{B}} , on ∂ ⁡ Ω × [ 0 , T ] {\partial\Omega\times[0,T]} . Then this result is applied to discuss the nature of the territorial refuges in periodic competitive environments.

中文翻译:

周期抛物线问题中的保护区

摘要 本文表征是否 Σ ∞ ≡ lim λ ↑ ∞ ⁡ σ ⁢ [ 𝒫 + λ ⁢ m ⁢ ( x , t ) , 𝔅 , QT ] \Sigma_{\infty}\lambda\lim_{\lambda\uparrow\ infty}\sigma[\mathcal{P}+\lambda m(% x,t),\mathfrak{B},Q_{T}] 是有限的,其中 m ⪈ 0 {m\gneq 0} 是 T 周期的,并且σ ⁢ [ 𝒫 + λ ⁢ m ⁢ ( x , t ) , 𝔅 , QT ] {\sigma[\mathcal{P}+\lambda m(x,t),\mathfrak{B},Q_{T}]}代表抛物线算子 𝒫 + λ ⁢ m ⁢ ( x , t ) {\mathcal{P}+\lambda m(x,t)} 在 QT ≡ Ω × [ 0 , T ] {Q_{T }\equiv\Omega\times[0,T]} 服从混合类型的一般边界算子 𝔅 {\mathfrak{B}} ,在 ∂ ⁡ Ω × [ 0 , T ] {\partial\Omega\times[ 0,T]}。然后将该结果应用于讨论周期性竞争环境中领土避难所的性质。
更新日期:2020-05-01
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