Título:	Multivalued dynamics of non-autonomous reaction–diffusion equation with nonlinear advection term
Autor(es):	Silva, Willian Cintra da Freitas, Mirelson Martins Ma, To Fu Marín-Rubio, Pedro
ORCID:	https://orcid.org/0000-0001-6437-3576 https://orcid.org/0000-0001-6942-3931 https://orcid.org/0000-0002-5746-6229 https://orcid.org/0000-0002-6215-1651
Afiliação do autor:	University of Brasília, Department of Mathematics Federal University of Pará University of Brasília, Department of Mathematics Universidad de Sevilla, Dpto. Ecuaciones Diferenciales y Análisis Numérico
Assunto:	Semicontinuidade superior Equação de reação-difusão
Data de publicação:	23-Jan-2024
Editora:	Elsevier
Referência:	SILVA, Willian Cintra da; FREITAS, Mirelson Martins; MA, To Fu; MARÍN-RUBIO, Pedro. Multivalued dynamics of non-autonomous reaction–diffusion equation with nonlinear advection term. Chaos, Solitons & Fractals, [S.l], v. 180, e114499, 2024. DOI: https://doi.org/10.1016/j.chaos.2024.114499. Disponível em: https://www.sciencedirect.com/science/article/pii/S096007792400050X?via%3Dihub. Acesso em: 19 ago 2025.
Abstract:	In this paper, we investigate a reaction–diffusion population model with a nonlinear advection term and a time-dependent force given by the equation 𝑢𝑡 − 𝛥𝑢 + ⃗𝛼 ⋅ ∇𝑢 𝑝 = 𝑓(𝑢) + ℎ(𝑡) in (𝜏, ∞) × 𝛺, subject to the boundary condition 𝑢 = 0 on (𝜏, ∞) × 𝜕𝛺. Here, 𝛺 ⊂ R𝑁 with 𝑁 ≥ 1 is a bounded domain with smooth boundary, 𝜏 ∈ R, ⃗𝛼 = (𝛼1 , …, 𝛼𝑁 ) is a given advective direction and 𝑝 > 1. The presence of the nonlinear advection term ⃗𝛼 ⋅ ∇𝑢 𝑝 introduces technical difficulties in the analysis, leading to a scenario where the uniqueness of weak solutions cannot be guaranteed. Consequently, the equation generates a multi-valued nonautonomous dynamical system. In this context, we establish the existence of minimal pullback attractors, considering universes of bounded and tempered sets. Moreover, we explore the relationships between these pullback attractors. Finally, we prove the upper semicontinuity of pullback attractors with respect to the advective vector ⃗𝛼 .
Unidade Acadêmica:	Instituto de Ciências Exatas (IE) Departamento de Matemática (IE MAT)
DOI:	https://doi.org/10.1016/j.chaos.2024.114499
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