Artículos (Análisis Matemático)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10809

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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). España
We 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.
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 grants
The 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.
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.
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 Competitividad
In 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.
Carreau law for non-newtonian fluid flow through a thin porous media
(Oxford Academic, 2022-03-21) Anguiano Moreno, María; Bonnivard, Matthieu; Suárez Grau, Francisco Javier; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM104: Analisis Matematico
We consider the flow of generalized Newtonian fluid through a thin porous media. The media under consideration is a bounded perforated three dimensional domain confined between two parallel plates, where the distance between the plates is described by a small parameter ⁠. The perforation consists in an array of solid cylinders, which connect the plates in perpendicular direction, with diameter of size and distributed periodically with period ⁠. The flow is described by the three dimensional incompressible stationary Stokes system with a nonlinear viscosity following the Carreau law. We study the limit when the thickness tends to zero and prove that the averaged velocity satisfies a nonlinear two-dimensional homogenized law of Carreau type. We illustrate our homogenization result by numerical simulations showing the influence of the Carreau law on the behavior of the limit system, in the case where the flow is driven by a constant pressure gradient and for different geometries of perforations.
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.
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). España
We 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.
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.
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 Andalucía
We 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.
Existence, uniqueness and global behavior of the solutions to some nonlinear vector equations in a finite dimensional Hilbert space
(Elsevier, 2017-09) Abdelli, Mama; Anguiano Moreno, María; Haraux, Alain; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM104: Análisis Matemático
The initial value problem and global properties of solutions are studied for the vectorequation:(∥u′∥lu′)′ + ∥A1/2u∥β Au + g(u′) = 0 in a finite dimensional Hilbert space under suitable assumptions on g.
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 Matematico
We 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.
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 Competitividad
We 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.
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 Matemático
We 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.
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). España
In 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.
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 Matematico
By 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.
Homogenization of parabolic problems with dynamical boundary conditions of reactive-diffusive type in perforated media
(Wiley, 2020-06-13) Anguiano Moreno, María; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM104: Analisis Matematico
This paper deals with the homogenization of the reaction-diffusion equations in a domain containing periodically distributed holes of size ε, with a dynamical boundary condition of reactive-diffusive type, i.e., we consider the following nonlinear boundary condition on the surface of the holes where denotes the Laplace–Beltrami operator on the surface of the holes, ν is the outward normal to the boundary, plays the role of a surface diffusion coefficient and g is the nonlinear term. We generalize our previous results established in the case of a dynamical boundary condition of pure-reactive type, i.e., with . We prove the convergence of the homogenization process to a nonlinear reaction-diffusion equation whose diffusion matrix takes into account the reactive-diffusive condition on the surface of the holes.
Lower-Dimensional Nonlinear Brinkman’s Law for Non-Newtonian Flows in a Thin Porous Medium
(Springer, 2021-06-01) Anguiano Moreno, María; Suárez Grau, Francisco Javier; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM104: Analisis Matematico
In this paper, we study the stationary incompressible power law fluid flow in a thin porous medium. The media under consideration is a bounded perforated 3D domain confined between two parallel plates, where the distance between the plates is very small. The perforation consists in an array solid cylinders, which connect the plates in perpendicular direction, distributed periodically with diameters of small size compared to the period. For a specific choice of the thickness of the domain, we found that the homogenization of the power law Stokes system results a lower-dimensional nonlinear Brinkman type law.
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 Matematico
In 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.
Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions
(American Institute of Mathematical Sciences, 2019-06) Anguiano Moreno, María; Suárez Grau, Francisco Javier; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Universidad de Sevilla. FQM104: Análisis Matemático
We consider the Stokes system in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size ε. On the boundary of the cylinders we prescribe non-homogeneous slip boundary conditions depending on a parameter γ. The aim is to give the asymptotic behavior of the velocity and the pressure of the fluid as ε goes to zero. Using an adaptation of the unfolding method, we give, following the values of γ, different limit systems.
Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary
(Oxford University Press, 2019) Anguiano Moreno, María; Suárez Grau, Francisco Javier; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Junta de Andalucía; Ministerio de Economía y Competitividad (MINECO). España; Universidad de Sevilla. FQM104: Análisis Matemático
We consider a non-Newtonian fluid flow in a thin domain with thickness ηε and an oscillating top boundary of period ε. The flow is described by the 3D incompressible Navier-Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index p, with 9/5 < p < +∞. We consider the limit when the thickness tends to zero and we prove that the three characteristic regimes for Newtonian fluids are still valid for non-Newtonian fluids, i.e. Stokes roughness (ηε ≈ ε), Reynolds roughness (ηε << ε) and high-frequency roughness (ηε >> ε) regime. Moreover, we obtain different nonlinear Reynolds-type equations in each case.

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Examinando Artículos (Análisis Matemático) por Autor "Anguiano Moreno, María"