Article
Multivalued dynamics of non-autonomous reaction-diffusion equation with nonlinear advection term
Author/s | Cintra da Silva, Willian
Freitas, Mirelson M. Ma, To Fu Marín Rubio, Pedro |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2024-03-02 |
Deposit Date | 2024-09-17 |
Published in |
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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
subject to the boundary condition
on
. Here,
with
is a bounded ... In this paper, we investigate a reaction–diffusion population model with a nonlinear advection term and a time-dependent force given by the equation subject to the boundary condition on . Here, with is a bounded domain with smooth boundary, , is a given advective direction and . The presence of the nonlinear advection term 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 . |
Citation | Cintra da Silva, W., Freitas, M.M., Ma, T.F. y Marín Rubio, P. (2024). Multivalued dynamics of non-autonomous reaction-diffusion equation with nonlinear advection term. Chaos, Solitons and Fractals, 180, 114499-1. https://doi.org/10.1016/j.chaos.2024.114499. |
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