Perfil del autor: Guillén González, Francisco Manuel
Datos institucionales
| Nombre | Guillén González, Francisco Manuel |
| Departamento | Ecuaciones Diferenciales y Análisis Numérico |
| Área de conocimiento | Análisis Matemático |
| Categoría profesional | Catedrático de Universidad |
| Correo electrónico | Solicitar |
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Estadísticas
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Nº publicaciones
105
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Nº visitas
11751
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Nº descargas
17828
| Publicaciones |
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Tesis Doctoral
 Analysis and optimal control for chemotaxis-consumption models
(2023)
En esta tesis investigamos el siguiente modelo de quimiotaxis-consumo en dominios acotados de RN (N = 1, 2, 3): ∂tu − Δu ... |
Trabajo Fin de Grado
Aplicación de redes neuronales al ajuste de parámetros en modelos diferenciales
(2023)
El éxito del desarrollo de la inteligencia artificial durante los últimos 15 años ha revolucionado todas las áreas del ... |
Artículo
Long-time behavior of global weak solutions for a beris-edwards type model of nematic liquid crystals
(Springer, 2022)
We consider a Beris-Edwards system modeling incompressible liquid crystal flows of nematic type. This system couples a ... |
Artículo
An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model
(Springer, 2022)
The design of numerical approximations of the Cahn-Hilliard model preserving the maximum principle is a challenging problem, ... |
Trabajo Fin de Grado
Aproximaciones numéricas descentradas para sistemas de EDP con quimiotaxis
(2022)
In this work, the phenomenon of chemotaxis is modeled, mainly by focusing on the Keller-Segel model, as well as other ... |
Trabajo Fin de Máster
Ecuaciones de coordenadas colectivas para una ecuación de tipo sine-Gordon. Análisis de fenómenos tipo ratchet en solitones topológicos
(2022)
The main aim of this project is to study the so-called soliton ratchet phenomena in a FrenkelKontorova model, by making ... |
Trabajo Fin de Grado
Modelización y simulaciones numéricas de problemas de control óptimo en modelos biológicos con quimiotaxis
(2022)
Mathematical modelling and numerical optimization are applications of Mathematics with a huge potencial, being able to ... |
Artículo
A Glioblastoma PDE-ODE model including chemotaxis and vasculature
(E.D.P. Sciences, 2022)
In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes chemotaxis term directed ... |
Artículo
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes
(Springer, 2021)
We consider the following repulsive-productive chemotaxis model: find 0, the cell density, and 0, the chemical concentration, ... |
Artículo
Comparison of two finite element schemes for a chemo-repulsion system with quadratic production
(Elsevier, 2021)
In this paper we propose two fully discrete Finite Elements (FE) schemes for a repulsive chemotaxis model with a quadratic ... |
Tesis Doctoral
Study of PDE-ODE Glioblastoma model with nonlinear diffusion and chemotaxis
(2021)
This thesis is dedicated to modeling and analyzing mathematically the development of Glioblastoma. Thanks to considering ... |
Artículo
A common framework for the robust design of tuned mass damper techniques to mitigate pedestrian-induced vibrations in lively footbridges
(Elsevier Ltd, 2021)
The dynamic response of modern slender footbridges is usually sensitive to both the pedestrian actions and the uncertainties ... |
Artículo
Fluid vesicles with internal nematic order
(Elsevier, 2020)
Models of flows containing vesicles membranes with liquid crystalline phases have been widely studied in recent times due ... |
Artículo
Nematic order on a deformable vesicle with anchoring effects
(Elsevier, 2020)
Models to represent the interactions of liquid crystalline phases with vesicles mem- branes have been widely studied in ... |
Artículo
Optimal bilinear control problem related to a chemo-repulsion system in 2D domains
(Société de Mathématiques Appliquées et Industrielles (SMAI), 2020)
In this paper, we study a bilinear optimal control problem associated to a chemo-repulsion model with linear production ... |
Artículo
A Regularity Criterion for a 3D Chemo-Repulsion System and Its Application to a Bilinear Optimal Control Problem
(SIAM, 2020)
In this paper, a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production is ... |
Artículo
Unconditionally energy stable fully discrete schemes for a chemo-repulsion model
(American Mathematical Society, 2019)
This work is devoted to studying unconditionally energy stable and mass-conservative numerical schemes for the following ... |
Artículo
Convergence to equilibrium of global weak solutions for a Cahn-Hilliard-Navier-Stokes vesicle model
(Springer, 2019)
In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in ... |
Artículo
From a cell model with active motion to a Hele–Shaw-like system: a numerical approach
(Springer, 2019)
In this paper we deal with the numerical solution of a Hele{Shaw-like system via a cell model with active motion. Convergence ... |
Trabajo Fin de Máster
Control de vibraciones de estructuras bajo incertidumbre
(2019)
Tanto la mejora de las propiedades resistentes de los materiales constructivos como los mayores requerimientos estéticos ... |
| Tesis Doctoral |
Artículo
Analysis of a chemo-repulsion model with nonlinear production: The continuous problem and unconditionally energy stable fully discrete schemes
(Cornell University, 2018)
We consider the following repulsive-productive chemotaxis model: Let p∈(1,2), find u≥0, the cell density, and v≥0, the ... |
Artículo
Convergence to equilibrium of global weak solutions for a Q-tensor problem related to liquid crystals
(Cornell University, 2018)
We study a Q-tensor problem modeling the dynamic of nematic liquid crystals in 3D domains. The system consists of the ... |
Libro
Recent Advances in PDEs: Analysis, Numerics and Control. In Honor of Prof. Fernández-Cara's 60th Birthday
(Springer, 2018)
This book contains the main results of the talks given at the workshop “Recent Advances in PDEs: Analysis, Numerics and ... |
Artículo
A projection-based time-splitting algorithm for approximating nematic liquid crystal flows with stretching
(Wiley, 2017)
A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic ... |
| Ponencia |
Artículo
Linear unconditional energy-stable splitting schemes for a phase-field model for nematic-isotropic flows with anchoring effects: L.U.E.S.S. SCHEMES FOR ISOTROPIC-NEMATIC FLOWS WITH ANCHORING EFFECTS
(Wiley, 2016)
Two-phase flows composed of fluids exhibiting different microscopic structure are an important class of engineering ... |
Artículo
On the stability of approximations for the Stokes problem using different finite element spaces for each component of the velocity
(Elsevier, 2016)
This paper studies the stability of velocity-pressure mixed approximations of the Stokes problem when different finite ... |
Artículo
Linear unconditional energy-stable splitting schemes for a phase-field model for Nematic-Isotropic flows with anchoring effects
(Wiley, 2016)
Two-phase flows composed of fluids exhibiting different microscopic structure are an important class of engineering ... |
| Ponencia |
Artículo
Approximation of Smectic-A liquid crystals
(Elsevier, 2015)
In this paper, we present energy-stable numerical schemes for a Smectic-A liquid crystal model. This model involve the ... |
| Ponencia |
Artículo
Analysis of the hydrostatic Stokes problem and finite-element approximation in unstructured meshes
(Springer, 2015)
The stability of velocity and pressure mixed finite-element approximations in general meshes of the hydrostatic Stokes ... |
Artículo
Numerical methods for solving the Cahn-Hilliard equation and its applicability to related Energy-based models
(Springer, 2015)
In this paper, we review some numerical methods presented in the literature in the last years to approximate the Cahn-Hilliard ... |
Artículo
Stabilized schemes for the hydrostatic Stokes equations
(Society for Industrial and Applied Mathematics, 2015)
Some new stable finite element (FE) schemes are presented for the hydrostatic Stokes system or primitive equations of the ... |
Artículo
Weak solutions for an initial-boundary Q-Tensor problem related to liquid crystals
(Elsevier, 2015)
The coupled Navier-Stokes and Q-Tensor system is considered in a bounded three-dimensional domain under homogeneous Dirichlet ... |
Artículo
A time-splitting finite-element stable approximation for the Ericksen-Leslie equations
(Society for Industrial and Applied Mathematics, 2015)
In this paper we propose an unconditional energy-stable time-splitting finite-element scheme for approximating the ... |
Capítulo de Libro
On the regularity of the Q-Tensor depending on the data
(Universidad de Zaragoza, 2015)
The coupled Navier-Stokes and Q-Tensor system is one of the models used to describe the behavior of the nematic liquid ... |
Artículo
A uniqueness and regularity criterion for Q-tensor models with Neumann boundary conditions
(Ohio University Press, 2014)
We give a regularity criterion for a Q-tensor system modeling a nematic Liquid Crystal, under homogeneous Neumann boundary ... |
Artículo
Convergence to equilibrium for smectic-A liquid crystals in 3D domains without constraints for the viscosity
(Elsevier, 2014)
In this paper, we focus on a smectic-A liquid crystal model in 3D domains, and obtain three main results: the proof of an ... |
Artículo
A review on mathematical analysis for nematic and smectic-A liquid crystal models
(Cambridge University Press, 2014)
We review the mathematical analysis of some uniaxial, liquid crystal phases. First, we state the models for the two di ... |
| Ponencia |
Capítulo de Libro
Some properties on the Q-Tensor system
(Universidad de Zaragoza, 2014)
We study the coupled Navier-Stokes and Q-Tensor system (analyzed in cf. [Paicu, M., and Zarnescu, A. Energy dissipation ... |
Artículo
Weak time regularity and uniqueness for a Q-Tensor model
(Society for Industrial and Applied Mathematics, 2014)
The coupled Navier-Stokes and Q-Tensor system is one of the models used to describe the behavior of the nematic liquid ... |
| Ponencia |
Artículo
A linear mixed finite element scheme for a nematic Ericksen-Leslie liquid crystal model
(Centre National de la Recherche Scientifique, 2013)
In this work we study a fully discrete mixed scheme, based on continuous finite elements in space and a linear semi-implicit ... |
Tesis Doctoral
Analysis and numerical simulation of fluids related to hydrostactic approximations
(2013)
Los modelos matemáticos de circulación global de la atmósfera y el océano terrestre han alcanzado una gran importancia en ... |
| Ponencia |
| Ponencia |
Artículo
On a double penalized smectic-A model
(American Institute of Mathematical Sciences, 2012)
In smectic-A liquid crystals a unity director vector n appear, modeling an average preferential direction of the molecules ... |
Tesis Doctoral
Análisis y Simulaciones Numéricas en Mecánica de Fluidos y Campos de Fase Numerical Analysis and Simulations for Fluid Mechanics and Phase-field Models
(2012)
Applied Mathematics research is expanding to encompass quantitative physical phenomena of growing importance. These ... |
Artículo
Superconvergence in velocity and pressure for the 3D time-dependent Navier-Stokes equations
(Sociedad Española de Matemática Aplicada, 2012)
This work is devoted to the superconvergence in space approximation of a fully discrete scheme for the incompressible ... |
Artículo
An overview on numerical analyses of nematic liquid crystal flows
(Springer, 2011)
The purpose of this work is to provide an overview of the most recent numerical developments in the field of nematic liquid ... |
Artículo
Finite element approximation of nematic liquid crystal flows using a saddle-point structure
(Elsevier, 2011)
In this work, we propose finite element schemes for the numerical approximation of nematic liquid crystal flows, based on ... |
Artículo
Error estimates of a linear decoupled Euler–FEM scheme for a mass diffusion model
(Springer, 2011)
We present error estimates of a linear fully discrete scheme for a threedimensional mass diffusion model for incompressible ... |
Artículo
Global in time solution and time-periodicity for a smectic-A liquid crystal model
(American Institute of Mathematical Sciences, 2010)
In this paper some results are obtained for a smectic-A liquid crystal model with time-dependent boundary Dirichlet data ... |
| Ponencia |
Artículo
Stability for nematic liquid crystals with stretching terms
(World Scientific, 2010)
We study a nematic crystal model appearing in [Liu et al.,2007] modeling stretching effects depending on the different ... |
Artículo
Convergence and error estimates of two iterative methods for the strong solution of the incompressible korteweg model
(World Scientific, 2009)
We show the existence of strong solutions for a fluid model with Korteweg tensor, which is obtained as limit of two iterative ... |
Artículo
Regularity and time-periodicity for a nematic liquid crystal model
(Elsevier, 2009)
In this paper two main results are obtained for a nematic liquid crystal model with timedependent boundary Dirichlet data ... |
Artículo
Sufficient conditions for regularity and uniqueness of a 3D nematic liquid crystal model
(Wiley, 2009)
In [3] L. C. Berselli, On a Regularity Criterion for the Solutions to the 3D Navier-Stokes Equations, Diff. and Integral ... |
Artículo
Método de elementos finitos para la aproximación de un modelo de cristales líquidos nemáticos
(Sociedad Española de Matemática Aplicada, 2009)
En esta charla analizamos la aproximación numérica con elementos finitos en espacio y diferencias finitas en tiempo de un ... |
Artículo
Reproductive solution for grade-two fluid model in two dimensions
(Universidad Industrial de Santander, 2009)
We treat the existence of reproductive solution (weak periodic solution) of a second-grade fluid system in two dimensions, by using the Galerkin approximation method and compactness arguments. |
Ponencia
Estabilidad asintótica para modelos de cristales líquidos nemáticos
(2009)
En este trabajo estudiamos el comportamiento asintótico en tiempo infinito y la estabilidad de soluciones de un sistema ... |
Artículo
Stability and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model
(EDP Sciences, 2009)
We analyze two numerical schemes of Euler type in time and C0 finite-element type with P1-approximation in space for solving ... |
Tesis Doctoral
Análisis numérico de esquemas fraccionados en tiempo para Navier-Stokes 3D y ecuaciones primitivas
(2008)
En esta Tesis nos centramos en el análisis numérico del método de descomposición de la viscosidad y del método de proyección ... |
Tesis Doctoral
Análisis numérico de algunos modelos diferenciales acoplados de la mecánica de fluidos
(2008)
La finalidad de esta tesis es aportar un mayor grado de entendimiento, desde el aspecto numérico, de diversos sistemas en ... |
Artículo
Conditional stability and convergence of a fully discrete scheme for three-dimensional Navier–Stokes equations with mass diffusion
(Society for Industrial and Applied Mathematics, 2008)
We construct a fully discrete numerical scheme for three-dimensional incompressible fluids with mass diffusion (in ... |
Artículo
 Unconditional stability and convergence of fully discrete schemes for 2D viscous fluids models with mass diffusion
(American Mathematical Society, 2008)
In this work we develop fully discrete (in time and space) numerical schemes for two-dimensional incompressible fluids ... |
Ponencia
Reproductive and time periodic solutions for incompressible fluids
(2007)
In this article, our aims is to review some of the results that are currently available concerning the existence, uniqueness ... |
Ponencia
Regularidad anisótropa de un problema de Ecuaciones Primitivas
(2007)
En este trabajo estudiamos la regularidad de las Ecuaciones Primitivas (EP) del Océano, con condición de contorno sobre ... |
Ponencia
Aproximación de un modelo de cristales líquidos nemáticos con un esquema completamente discreto y penalizado
(2007)
En esta comunicación proponemos y analizamos un esquema numérico totalmente discreto con elementos finitos en espacio y ... |
Ponencia
Time-periodic solutions for a generalized Boussinesq model with Neumann boundary conditions for temperature
(Royal Society of London, 2007)
The aim of this work is to prove the existence of regular time-periodic solutions for a generalized Boussinesq model (with ... |
Ponencia
Error estimates of optimal order in a fractional-step scheme for the 3D Navier-Stokes equations
(2007)
We present some improvements on the error estimates obtained by J.Blasco and R.Codina for a viscosity-splitting in time ... |
Artículo
A review on reproductivity and time periodicity for incompressible fluids
(Sociedad Española de Matemática Aplicada, 2007)
In this article, our aims is to review some of the results that are currently available concerning the existence, uniqueness ... |
| Ponencia |
Artículo
Reproductivity for a nematic liquid crystal model
(2006)
In this paper we prove existence of weak solution with the reproductivity in time property, for a penalized PDE's system ... |
| Ponencia |
| Ponencia |
Artículo
Local strong solution for the incompressible Korteweg model
(Elsevier, 2006)
We consider a Navier-Stokes type system with a Korteweg stress tensor, coupled with a concentration equation without ... |
| Ponencia |
| Ponencia |
Artículo
Local and global strong solution by the semi-Galerkin method for the model of mass diffusion
(Sociedade Brasileira de Matemática, 2006)
In this work, we present some results for local and global in time solutions (defined in the time interval (0, T) with T ... |
Artículo
On the uniqueness and regularity of the Primitive Equations imposing additional anisotropic regularity
(Elsevier, 2005)
In this note, we prove that given u a weak solution of the Primitive Equations, imposing an additional condition on the ... |
| Artículo |
Ponencia
Regular time-reproductive solutions for generalized Boussinesq model with Neumann boundary conditions for temperature
(2005)
The aim of this work is to prove existence of regular time reproductive solutions for a generalized Boussinesq model (with ... |
Artículo
A review on the improved regularity for the primitive equations
(2005)
In this work we will study, some types of regularity properties of solutions for the geophysical model of hydrostatic ... |
Artículo
A corrector for the Sverdrup solution for a domain with islands
(Taylor & Francis, 2004)
In this paper we look at the influence of the Coriolis force on the quasi-geostrophic equations on a domain with islands. ... |
Ponencia
Optimal control and partial differential equations
(2004)
In this work, some type of optimal control problems with equality constraints given by Partial Differential Equations (PDE) ... |
Artículo
Hydrostatic Stokes equations with non-smooth data for mixed boundary conditions
(Elsevier, 2004)
The main subject of this work is to study the concept of very weak solution for the hydrostatic Stokes system with mixed ... |
Artículo
Density-dependent incompressible fluids with non-Newtonian viscosity
(Institute of Mathematics, Czech Academy of Sciences, 2004)
We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant ... |
Artículo
A note on a degenerate elliptic equation with applications for lakes and seas
(Texas State University, 2004)
In this paper, we give an intermediate regularity result on a degenerate elliptic equation with a weight blowing up on the ... |
Artículo
Asymptotic derivation of a Navier condition for the primitive equations
(IOS Press, 2003)
This paper is devoted to the establishment of a friction boundary condition associated with hydrostatic Navier-Stokes ... |
Artículo
On the uniqueness of weak solutions of the two-dimensional primitive equations
(Ohio University Press, 2003)
The uniqueness of weak solutions of the primitive equations with Dirichlet boundary conditions at the bottom is an open ... |
Artículo
Global solution of nematic liquid crystals models
(Elsevier, 2002)
We prove existence of a global weak solution for a nematic liquid crystal problem by means of a penalization method using a simplified Ericksen-Leslie model and a new compactness property for the gradient of the director field. |
Artículo
On the strong solutions of the primitive equations in 2D domains
(Elsevier, 2002)
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Artículo
Sobre la regularidad, unicidad y justificación asintótica del problema de Ecuaciones Primitivas del Océano
(Sociedad Española de Matemática Aplicada, 2002)
En este trabajo exponemos, y comentamos brevemente, los resultados obtenidos en la Tesis Doctoral de M. A. Rodríguez ... |
Artículo
Global in time solutions for the Poiseuille flow of Oldroyd type in 3D domains
(Springer-Verlag, 2001)
A Poiseuille flow in a 3D cylindrical domain is considered for a non-newtonian fluid of Oldroyd type. We prove existence ... |
Artículo
On the singular times of fluids with nonlinear viscosity
(Elsevier, 2001)
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| Tesis Doctoral |
Artículo
Anisotropic estimates and strong solutions of the primitive equations
(Ohio University Press, 2001)
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Artículo
Mathematical justification of the hydrostatic approximation in the primitive equations of geophysical fluid dynamics
(Society for Industrial and Applied Mathematics, 2001)
Geophysical fluids all exhibit a common feature: their aspect ratio (depth to horizontal width) is very small. This leads ... |
Ponencia
Uniqueness of solution for the 2D Primitive Equations with friction condition on the bottom
(2001)
Uniqueness of solution for the Primitive Equations with Dirichlet conditions on the bottom is an open problem even in 2D ... |
Tesis Doctoral
Contribución al estudio teórico de algunas E.D.P. no lineales relacionadas con fluidos no newtonianos
(1995)
El objetivo básico de esta Memoria es aportar nuevos resultados teóricos de existencia, unicidad y dependencia continua ... |
Tesis Doctoral
Nuevos resultados sobre el problema de Navier-Stokes con densidad variable y algunas variantes: Existencia, unicidad, otros resultados teóricos y aproximación numérica
(1992)
Haremos a continuación una breve descripción de cada uno de los Capítulos de los que consta esta Memoria. Comenzamos el ... |