Artículos (Análisis Matemático)
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Artículo Approximate fixed points in metric spaces(2024-06-15) Espínola García, Rafael; Kirk, William A.; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM127: Análisis Funcional no LinealThe chances for a mapping taken at random from a given set of mappings to have approximate fixed points are studied in this paper. We start from the discrete case to range more abstract spaces as metric measure spaces. Initial insights for this work are elementary, and some of the observations may already be known. At the same time, they seem to point the way to deeper questions and raise the potential for future study.Artículo Qué tienen de especiales las funciones especiales(Real Academia Sevillana de Ciencias, 2022) Durán Guardeño, Antonio José; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM262: Teoria de la AproximacionArtículo Homogenization of a non-stationary non-Newtonian flow in a porous medium containing a thin fissure(Cambridge University Press, 2018-02-05) Anguiano Moreno, María; Universidad de Sevilla. Departamento de Análisis MatemáticoWe consider a non-stationary incompressible non-Newtonian Stokes system in a porous medium with characteristic size of the pores ε and containing a thin fissure of width ηε. The viscosity is supposed to obey the power law with flow index 5/3 ≤ q ≤ 2. The limit when size of the pores tends to zero gives the homogenized behavior of the flow. We obtain three different models depending on the magnitude ηε with respect to ε: if ηε ≪ ε^{q/(2q−1)} the homogenized fluid flow is governed by a time-dependent nonlinear Darcy law, while if ηε ≫ ε^{q/(2q−1)} is governed by a time-dependent nonlinear Reynolds problem. In the critical case, ηε ≈ ε^{q/(2q−1)} , the flow is described by a time-dependent nonlinear Darcy law coupled with a time-dependent nonlinear Reynolds problem.Artículo Asymptotic behaviour of the nonautonomous SIR equations with diffusion(American Institute of Mathematical Sciences (AIMS), 2014) Anguiano Moreno, María; Kloeden, Peter E.; Universidad de Sevilla. Departamento de Análisis Matemático; DFG grants; Ministerio de Economía y Competitividad (MINECO). España; Junta de Andalucía Ayuda Incentivos Actividades Científicas; Junta de Andalucía Proyecto de Excelencia; Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía)The existence and uniqueness of positive solutions of a nonautonomous system of SIR equations with diffusion are established as well as the continuous dependence of such solutions on initial data. The proofs are facilitated by the fact that the nonlinear coefficients satisfy a global Lipschitz property due to their special structure. An explicit disease-free nonautonomous equilibrium solution is determined and its stability investigated. Uniform weak disease persistence is also shown. The main aim of the paper is to establish the existence of a nonautonomous pullback attractor is established for the nonautonomous process generated by the equations on the positive cone of an appropriate function space. For this an energy method is used to determine a pullback absorbing set and then the flattening property is verified, thus giving the required asymptotic compactness of the process.Artículo On the non-stationary non-Newtonian flow through a thin porous medium(Wiley, 2017) Anguiano Moreno, María; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de Andalucía; European Research Council (ERC)We consider a non-stationary incompressible non-Newtonian flow in a thin porous medium of thickness ε which is perforated by periodically distributed solid cylinders of size aε. The viscosity is supposed to obey the power law with flow index 3/2 < p < 2 (pseudoplastic fluids). The limit when the thickness tends to zero is considered. Time-dependent Darcy’s laws are rigorously derived from this model depending on the magnitude aε with respect to ε.Artículo Attractors for a non-autonomous Liénard equation(World Scientific Publishing, 2015) Anguiano Moreno, María; Universidad de Sevilla. Departamento de Análisis Matemático; V Plan Propio de Investigación de la Universidad de Sevilla; Fondo Europeo de Desarrollo Regional and Ministerio de Economía y CompetitividadIn this paper we prove the existence of pullback and uniform attractors for a non-autonomous Liénard equation. The relation among these attractors is also discussed. After that, we consider that the Liénard equation includes forcing terms which belong to a class of functions extending periodic and almost peri- odic functions recently introduced by Kloeden and Rodrigues in [14]. Finally, we estimate the Hausforff dimension of the pullback attractor. We illustrate these results with a numerical simulation: we present a simulation showing the pullback attractor for the non-autonomous Van der Pol equation, an important special case of the non-autonomous Liénard equation.Artículo Asymptotic behaviour of nonlocal reaction-diffusion equations(Elsevier, 2010) Anguiano Moreno, María; Kloeden, Peter E.; Lorenz, Thomas; Universidad de Sevilla. Departamento de Análisis Matemático; Ministerio de Ciencia y Tecnología; DFG grantsThe existence of a global attractor in L^2(Ω) is established for a reaction-diffusion equation on a bounded domain Ω in R^d with Dirichlet boundary conditions, where the reaction term contains an operator F : L^2(Ω) → L^2(Ω) which is nonlocal and possibly nonlinear. Existence of weak solutions is established, but uniqueness is not required. Compactness of the multivalued flow is obtained via estimates obtained from limits of Galerkin approximations. In contrast with the usual situation, these limits apply for all and not just for almost all time instants.Artículo Analysis of the effects of a fissure for a non-Newtonian fluid flow in a porous medium(International Press, 2018) Anguiano Moreno, María; Suárez Grau, Francisco Javier; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de Andalucía; Ministerio de Economía y Competitividad (MINECO). EspañaWe study the solution of a non-Newtonian flow in a porous medium which characteristic size of the pores ε and containing a fissure of width ηε. The flow is described by the incompressible Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index 1 < r < +∞. We consider the limit when size of the pores tends to zero and we obtain different models depending on the magnitude ηε with respect to ε.Artículo Homogenization of an incompressible non-Newtonian flow through a thin porous medium(Springer, 2017) Anguiano Moreno, María; Suárez Grau, Francisco Javier; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de Andalucía; European Research Council (ERC); Ministerio de Economía y Competitividad (MINECO). EspañaIn this paper, we consider a non-Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically solid cylinders of size aε. The flow is described by the 3D incompressible Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index 1 < p < +∞. We consider the limit when domain thickness tends to zero and we obtain different models depending on the magnitude aε with respect to ε.Artículo Derivation of a coupled Darcy-Reynolds equation for a fluid flow in a thin porous medium including a fissure(Springer, 2017) Anguiano Moreno, María; Suárez Grau, Francisco Javier; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de Andalucía; European Research Council (ERC); Ministerio de Economía y Competitividad (MINECO). EspañaWe study the asymptotic behavior of a fluid flow in a thin porous medium of thickness ε, which characteristic size of the pores ε, and containing a fissure of width ηε. We consider the limit when the size of the pores tends to zero and we find a critical size ηε ≈ ε^{2/3} in which the flow is described by a 2D Darcy law coupled with a 1D Reynolds problem. We also discuss the other cases.Artículo On the Kneser property for reaction-diffusion equations in some unbounded domains with an H^{-1}-valued non-autonomous forcing term(Elsevier, 2012) Anguiano Moreno, María; Morillas Jurado, Francisco; Valero Cuadra, José; Universidad de Sevilla. Departamento de Análisis Matemático; Ministerio de Ciencia e Innovación (MICIN). España; Junta de Andalucía; Comunidad Autónoma de MurciaIn this paper we prove the Kneser property for a reaction-diffusion equation on an unbounded domain satisfying the Poincaré inequality with an external force taking values in the space H^{−1}. Using this property of solutions we check also the connectedness of the associated global pullback attractor. We study also similar properties for systems of reaction-diffusion equations in which the domain is the whole R^N. Finally, the results are applied to a generalized logistic equation.Artículo Derivation of a quasi-stationary coupled Darcy-Reynolds equation for incompressible viscous fluid flow through a thin porous medium with a fissure(Wiley, 2017) Anguiano Moreno, María; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de Andalucía; European Research Council (ERC)We consider a non-stationary Stokes system in a thin porous medium of thickness ε which is perforated by periodically distributed solid cylinders of size ε, and containing a fissure of width ηε. Passing to the limit when ε goes to zero, we find a critical size ηε ≈ ε^{2/3} in which the flow is described by a 2D quasi-stationary Darcy law coupled with a 1D quasi-stationary Reynolds problem.Artículo Darcy's laws for non-stationary viscous fluid flow in a thin porous medium(Wiley, 2017) Anguiano Moreno, María; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de Andalucía; European Research Council (ERC)We consider a non-stationary Stokes system in a thin porous medium Ωε of thickness ε which is perforated by periodically solid cylinders of size aε. We are interested here to give the limit behavior when ε goes to zero. To do so, we apply an adaptation of the unfolding method. Time-dependent Darcy’s laws are rigorously derived from this model depending on the comparison between aε and ε.Artículo The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium(Springer, 2018) Anguiano Moreno, María; Suárez Grau, Francisco Javier; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de Andalucía; Ministerio de Economía y Competitividad (MINECO). EspañaWe consider a Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size aε. Generalizing [2], the fluid is described by the 3D incompressible Navier-Stokes system where the external force takes values in the space H^{−1}, and the porous medium considered has one of the most commonly used distribution of cylinders: hexagonal distribution. By means of an adaptation of the unfolding method, three different Darcy’s laws are rigorously derived from this model depending on the magnitude aε with respect to ε.Artículo Existence and estimation of the Hausdorff dimension of attractors for an epidemic model(Wiley, 2017) Anguiano Moreno, María; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de AndalucíaWe prove the existence of pullback and uniform attractors for the process associated to a non-autonomous SIR model, with several types of non-autonomous features. The Hausdorff dimension of the pullback attractor is also estimated. We illustrate some examples of pullback attractors by numerical simulations.Artículo Pullback attractors for a reaction-diffusion equation in a general nonempty open subset of R^N with non-autonomous forcing term in H^{−1}(World Scientific Publishing, 2015) Anguiano Moreno, María; Universidad de Sevilla. Departamento de Análisis MatemáticoThe existence of minimal pullback attractors in L^2(Ω) for a non-autonomous reaction-diffusion equation, in the frameworks of universes of fixed bounded sets and that given by a tempered growth condition, is proved in this paper, when the domain Ω is a general nonempty open subset of R^N, and h ∈ L^2_loc(R;H^{−1}(Ω)). The main concept used in the proof is the asymptotic com- pactness of the process generated by the problem. The relation among these families is also discussed.Artículo H^2-boundedness of the pullback attractor for the non-autonomous SIR equations with diffusion(Elsevier, 2015) Anguiano Moreno, María; Universidad de Sevilla. Departamento de Análisis Matemático; Fondo Europeo de Desarrollo Regional and Ministerio de Economía y CompetitividadWe prove some regularity results for the pullback attractor of a non- autonomous SIR model with diffusion in a bounded domain Ω of Rd where d ≥ 1. We show a regularity result for the unique solution of the prob- lem. We establish a general result about (H^2(Ω))^3-boundedness of invariant sets for the associate evolution process. Then, as a consequence, we de- duce that the pullback attractor of the non-autonomous system of SIR equations with diffusion is bounded in (H^2 (Ω))^3.
Artículo Mathematical derivation of a Reynolds equation for magneto-micropolar fluid flows through a thin domain(Springer, 2024-01-28) Anguiano Moreno, María; Suárez Grau, Francisco Javier; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM104: Analisis MatematicoIn this paper, we study the asymptotic behavior of the stationary 3D magneto-micropolar fluid flow through a thin domain, whose thickness is given by a parameter . Assuming that the magnetic Reynolds number is written in terms of the thickness , we prove that there exists a critical magnetic Reynolds number, namely , such that for every magnetic Reynolds number with order smaller or equal than , the magneto-micropolar fluid flow in the thin domain can be modeled asymptotically when tends to zero by a 2D Reynolds-like model, whose expression is also given.Artículo Homogenization of Bingham flow in thin porous media(AIMS, 2019-12-01) Anguiano Moreno, María; Bunoiu, Renata; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM104: Analisis MatematicoBy using dimension reduction and homogenization techniques, we study the steady flow of an incompresible viscoplastic Bingham fluid in a thin porous medium. A main feature of our study is the dependence of the yield stress of the Bingham fluid on the small parameters describing the geometry of the thin porous medium under consideration. Three different problems are obtained in the limit when the small parameter tends to zero, following the ratio between the height of the porous medium and the relative dimension of its periodically distributed pores. We conclude with the interpretation of these limit problems, which all preserve the nonlinear character of the flow.Artículo Existence, Uniqueness and Homogenization of Nonlinear Parabolic Problems with Dynamical Boundary Conditions in Perforated Media(Springer, 2019-12-03) Anguiano Moreno, María; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM104: Analisis MatematicoWe consider a nonlinear parabolic problem with nonlinear dynamical boundary conditions of pure-reactive type in a media perforated by periodically distributed holes of size . The novelty of our work is to consider a nonlinear model where the nonlinearity also appears in the boundary. The existence and uniqueness of solution is analyzed. Moreover, passing to the limit when goes to zero, a new nonlinear parabolic problem defined on a unified domain without holes with zero Dirichlet boundary condition and with extra terms coming from the influence of the nonlinear dynamical boundary conditions is rigorously derived.