Multivalued dynamics of non-autonomous reaction–diffusion equation with nonlinear advection term

Silva, Willian Cintra da; Freitas, Mirelson Martins; Ma, To Fu; Marín-Rubio, Pedro

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dc.contributor.author	Silva, Willian Cintra da	-
dc.contributor.author	Freitas, Mirelson Martins	-
dc.contributor.author	Ma, To Fu	-
dc.contributor.author	Marín-Rubio, Pedro	-
dc.date.accessioned	2025-09-25T13:51:32Z	-
dc.date.available	2025-09-25T13:51:32Z	-
dc.date.issued	2024-01-23	-
dc.identifier.citation	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.	pt_BR
dc.identifier.uri	http://repositorio.unb.br/handle/10482/52513	-
dc.language.iso	eng	pt_BR
dc.publisher	Elsevier	pt_BR
dc.rights	Acesso Restrito	pt_BR
dc.title	Multivalued dynamics of non-autonomous reaction–diffusion equation with nonlinear advection term	pt_BR
dc.type	Artigo	pt_BR
dc.subject.keyword	Semicontinuidade superior	pt_BR
dc.subject.keyword	Equação de reação-difusão	pt_BR
dc.identifier.doi	https://doi.org/10.1016/j.chaos.2024.114499	pt_BR
dc.description.abstract1	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 .	pt_BR
dc.identifier.orcid	https://orcid.org/0000-0001-6437-3576	pt_BR
dc.identifier.orcid	https://orcid.org/0000-0001-6942-3931	pt_BR
dc.identifier.orcid	https://orcid.org/0000-0002-5746-6229	pt_BR
dc.identifier.orcid	https://orcid.org/0000-0002-6215-1651	pt_BR
dc.contributor.affiliation	University of Brasília, Department of Mathematics	pt_BR
dc.contributor.affiliation	Federal University of Pará	pt_BR
dc.contributor.affiliation	University of Brasília, Department of Mathematics	pt_BR
dc.contributor.affiliation	Universidad de Sevilla, Dpto. Ecuaciones Diferenciales y Análisis Numérico	pt_BR
dc.description.unidade	Instituto de Ciências Exatas (IE)	pt_BR
dc.description.unidade	Departamento de Matemática (IE MAT)	pt_BR
Collection(s) :	Artigos publicados em periódicos e afins