Author profile: Guillén González, Francisco Manuel
Institutional data
| Name | Guillén González, Francisco Manuel |
| Department | Ecuaciones Diferenciales y Análisis Numérico |
| Knowledge area | Análisis Matemático |
| Professional category | Catedrático de Universidad |
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Statistics
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No. publications
101
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No. visits
9969
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No. downloads
13171
| Publications |
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Final Degree Project
 Aproximaciones numéricas descentradas para sistemas de EDP con quimiotaxis
(2022-06-22)
In this work, the phenomenon of chemotaxis is modeled, mainly by focusing on the Keller-Segel model, as well as other ... |
Master's Final Project
Ecuaciones de coordenadas colectivas para una ecuación de tipo sine-Gordon. Análisis de fenómenos tipo ratchet en solitones topológicos
(2022-06-15)
The main aim of this project is to study the so-called soliton ratchet phenomena in a FrenkelKontorova model, by making ... |
Final Degree Project
Modelización y simulaciones numéricas de problemas de control óptimo en modelos biológicos con quimiotaxis
(2022-06-01)
Mathematical modelling and numerical optimization are applications of Mathematics with a huge potencial, being able to ... |
Article
A Glioblastoma PDE-ODE model including chemotaxis and vasculature
(E.D.P. Sciences, 2022-01-26)
In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes chemotaxis term directed ... |
Article
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes
(Springer, 2021-12-10)
We consider the following repulsive-productive chemotaxis model: find 0, the cell density, and 0, the chemical concentration, ... |
Article
Comparison of two finite element schemes for a chemo-repulsion system with quadratic production
(Elsevier, 2021-12-07)
In this paper we propose two fully discrete Finite Elements (FE) schemes for a repulsive chemotaxis model with a quadratic ... |
PhD Thesis
Study of PDE-ODE Glioblastoma model with nonlinear diffusion and chemotaxis
(2021-11-29)
This thesis is dedicated to modeling and analyzing mathematically the development of Glioblastoma. Thanks to considering ... |
Article
A common framework for the robust design of tuned mass damper techniques to mitigate pedestrian-induced vibrations in lively footbridges
(Elsevier Ltd, 2021-01-01)
The dynamic response of modern slender footbridges is usually sensitive to both the pedestrian actions and the uncertainties ... |
Article
Fluid vesicles with internal nematic order
(Elsevier, 2020-10-22)
Models of flows containing vesicles membranes with liquid crystalline phases have been widely studied in recent times due ... |
Article
Nematic order on a deformable vesicle with anchoring effects
(Elsevier, 2020-04-16)
Models to represent the interactions of liquid crystalline phases with vesicles mem- branes have been widely studied in ... |
Article
Optimal bilinear control problem related to a chemo-repulsion system in 2D domains
(Société de Mathématiques Appliquées et Industrielles (SMAI), 2020-03-01)
In this paper, we study a bilinear optimal control problem associated to a chemo-repulsion model with linear production ... |
Article
A Regularity Criterion for a 3D Chemo-Repulsion System and Its Application to a Bilinear Optimal Control Problem
(SIAM, 2020-01-15)
In this paper, a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production is ... |
Article
Unconditionally energy stable fully discrete schemes for a chemo-repulsion model
(American Mathematical Society, 2019-09-01)
This work is devoted to studying unconditionally energy stable and mass-conservative numerical schemes for the following ... |
Article
Convergence to equilibrium of global weak solutions for a Cahn-Hilliard-Navier-Stokes vesicle model
(Springer, 2019-08-01)
In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in ... |
Master's Final Project
Control de vibraciones de estructuras bajo incertidumbre
(2019-01-01)
Tanto la mejora de las propiedades resistentes de los materiales constructivos como los mayores requerimientos estéticos ... |
Article
From a cell model with active motion to a Hele–Shaw-like system: a numerical approach
(Springer, 2019-01-01)
In this paper we deal with the numerical solution of a Hele{Shaw-like system via a cell model with active motion. Convergence ... |
| PhD Thesis |
Article
Analysis of a chemo-repulsion model with nonlinear production: The continuous problem and unconditionally energy stable fully discrete schemes
(Cornell University, 2018-08-21)
We consider the following repulsive-productive chemotaxis model: Let p∈(1,2), find u≥0, the cell density, and v≥0, the ... |
Article
Convergence to equilibrium of global weak solutions for a Q-tensor problem related to liquid crystals
(Cornell University, 2018-05-07)
We study a Q-tensor problem modeling the dynamic of nematic liquid crystals in 3D domains. The system consists of the ... |
Book
Recent Advances in PDEs: Analysis, Numerics and Control. In Honor of Prof. Fernández-Cara's 60th Birthday
(Springer, 2018-01-01)
This book contains the main results of the talks given at the workshop “Recent Advances in PDEs: Analysis, Numerics and ... |
Article
A projection-based time-splitting algorithm for approximating nematic liquid crystal flows with stretching
(Wiley, 2017-01-01)
A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic ... |
| Presentation |
Article
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, 2016-01-26)
Two-phase flows composed of fluids exhibiting different microscopic structure are an important class of engineering ... |
Article
Linear unconditional energy-stable splitting schemes for a phase-field model for Nematic-Isotropic flows with anchoring effects
(Wiley, 2016-01-01)
Two-phase flows composed of fluids exhibiting different microscopic structure are an important class of engineering ... |
| Presentation |
Article
On the stability of approximations for the Stokes problem using different finite element spaces for each component of the velocity
(Elsevier, 2016-01-01)
This paper studies the stability of velocity-pressure mixed approximations of the Stokes problem when different finite ... |
Article
Approximation of Smectic-A liquid crystals
(Elsevier, 2015-06-15)
In this paper, we present energy-stable numerical schemes for a Smectic-A liquid crystal model. This model involve the ... |
| Presentation |
Article
Analysis of the hydrostatic Stokes problem and finite-element approximation in unstructured meshes
(Springer, 2015-06-01)
The stability of velocity and pressure mixed finite-element approximations in general meshes of the hydrostatic Stokes ... |
Article
Numerical methods for solving the Cahn-Hilliard equation and its applicability to related Energy-based models
(Springer, 2015-04-01)
In this paper, we review some numerical methods presented in the literature in the last years to approximate the Cahn-Hilliard ... |
Article
A time-splitting finite-element stable approximation for the Ericksen-Leslie equations
(Society for Industrial and Applied Mathematics, 2015-01-01)
In this paper we propose an unconditional energy-stable time-splitting finite-element scheme for approximating the ... |
Chapter of Book
On the regularity of the Q-Tensor depending on the data
(Universidad de Zaragoza, 2015-01-01)
The coupled Navier-Stokes and Q-Tensor system is one of the models used to describe the behavior of the nematic liquid ... |
Article
Stabilized schemes for the hydrostatic Stokes equations
(Society for Industrial and Applied Mathematics, 2015-01-01)
Some new stable finite element (FE) schemes are presented for the hydrostatic Stokes system or primitive equations of the ... |
Article
Weak solutions for an initial-boundary Q-Tensor problem related to liquid crystals
(Elsevier, 2015-01-01)
The coupled Navier-Stokes and Q-Tensor system is considered in a bounded three-dimensional domain under homogeneous Dirichlet ... |
Article
A uniqueness and regularity criterion for Q-tensor models with Neumann boundary conditions
(Ohio University Press, 2014-11-01)
We give a regularity criterion for a Q-tensor system modeling a nematic Liquid Crystal, under homogeneous Neumann boundary ... |
Article
Convergence to equilibrium for smectic-A liquid crystals in 3D domains without constraints for the viscosity
(Elsevier, 2014-06-01)
In this paper, we focus on a smectic-A liquid crystal model in 3D domains, and obtain three main results: the proof of an ... |
Article
A review on mathematical analysis for nematic and smectic-A liquid crystal models
(Cambridge University Press, 2014-02-01)
We review the mathematical analysis of some uniaxial, liquid crystal phases. First, we state the models for the two di ... |
Chapter of Book
Some properties on the Q-Tensor system
(Universidad de Zaragoza, 2014-01-01)
We study the coupled Navier-Stokes and Q-Tensor system (analyzed in cf. [Paicu, M., and Zarnescu, A. Energy dissipation ... |
Article
Weak time regularity and uniqueness for a Q-Tensor model
(Society for Industrial and Applied Mathematics, 2014-01-01)
The coupled Navier-Stokes and Q-Tensor system is one of the models used to describe the behavior of the nematic liquid ... |
| Presentation |
| Presentation |
Article
A linear mixed finite element scheme for a nematic Ericksen-Leslie liquid crystal model
(Centre National de la Recherche Scientifique, 2013-09-01)
In this work we study a fully discrete mixed scheme, based on continuous finite elements in space and a linear semi-implicit ... |
PhD Thesis
Analysis and numerical simulation of fluids related to hydrostactic approximations
(2013-06-24)
Los modelos matemáticos de circulación global de la atmósfera y el océano terrestre han alcanzado una gran importancia en ... |
| Presentation |
| Presentation |
Article
On a double penalized smectic-A model
(American Institute of Mathematical Sciences, 2012-12-01)
In smectic-A liquid crystals a unity director vector n appear, modeling an average preferential direction of the molecules ... |
PhD Thesis
Análisis y Simulaciones Numéricas en Mecánica de Fluidos y Campos de Fase Numerical Analysis and Simulations for Fluid Mechanics and Phase-field Models
(2012-01-01)
Applied Mathematics research is expanding to encompass quantitative physical phenomena of growing importance. These ... |
Article
Superconvergence in velocity and pressure for the 3D time-dependent Navier-Stokes equations
(Sociedad Española de Matemática Aplicada, 2012-01-01)
This work is devoted to the superconvergence in space approximation of a fully discrete scheme for the incompressible ... |
Article
An overview on numerical analyses of nematic liquid crystal flows
(Springer, 2011-09-01)
The purpose of this work is to provide an overview of the most recent numerical developments in the field of nematic liquid ... |
Article
Finite element approximation of nematic liquid crystal flows using a saddle-point structure
(Elsevier, 2011-02-20)
In this work, we propose finite element schemes for the numerical approximation of nematic liquid crystal flows, based on ... |
Article
Error estimates of a linear decoupled Euler–FEM scheme for a mass diffusion model
(Springer, 2011-01-01)
We present error estimates of a linear fully discrete scheme for a threedimensional mass diffusion model for incompressible ... |
Article
Stability for nematic liquid crystals with stretching terms
(World Scientific, 2010-01-01)
We study a nematic crystal model appearing in [Liu et al.,2007] modeling stretching effects depending on the different ... |
Article
Global in time solution and time-periodicity for a smectic-A liquid crystal model
(American Institute of Mathematical Sciences, 2010-01-01)
In this paper some results are obtained for a smectic-A liquid crystal model with time-dependent boundary Dirichlet data ... |
| Presentation |
Article
Convergence and error estimates of two iterative methods for the strong solution of the incompressible korteweg model
(World Scientific, 2009-09-01)
We show the existence of strong solutions for a fluid model with Korteweg tensor, which is obtained as limit of two iterative ... |
Article
Regularity and time-periodicity for a nematic liquid crystal model
(Elsevier, 2009-07-01)
In this paper two main results are obtained for a nematic liquid crystal model with timedependent boundary Dirichlet data ... |
Article
Sufficient conditions for regularity and uniqueness of a 3D nematic liquid crystal model
(Wiley, 2009-06-01)
In [3] L. C. Berselli, On a Regularity Criterion for the Solutions to the 3D Navier-Stokes Equations, Diff. and Integral ... |
Article
Reproductive solution for grade-two fluid model in two dimensions
(Universidad Industrial de Santander, 2009-01-01)
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. |
Presentation
Estabilidad asintótica para modelos de cristales líquidos nemáticos
(2009-01-01)
En este trabajo estudiamos el comportamiento asintótico en tiempo infinito y la estabilidad de soluciones de un sistema ... |
Article
Método de elementos finitos para la aproximación de un modelo de cristales líquidos nemáticos
(Sociedad Española de Matemática Aplicada, 2009-01-01)
En esta charla analizamos la aproximación numérica con elementos finitos en espacio y diferencias finitas en tiempo de un ... |
Article
Stability and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model
(EDP Sciences, 2009-01-01)
We analyze two numerical schemes of Euler type in time and C0 finite-element type with P1-approximation in space for solving ... |
PhD Thesis
Análisis numérico de esquemas fraccionados en tiempo para Navier-Stokes 3D y ecuaciones primitivas
(2008-09-26)
En esta Tesis nos centramos en el análisis numérico del método de descomposición de la viscosidad y del método de proyección ... |
PhD Thesis
Análisis numérico de algunos modelos diferenciales acoplados de la mecánica de fluidos
(2008-01-09)
La finalidad de esta tesis es aportar un mayor grado de entendimiento, desde el aspecto numérico, de diversos sistemas en ... |
Article
 Unconditional stability and convergence of fully discrete schemes for 2D viscous fluids models with mass diffusion
(American Mathematical Society, 2008-01-01)
In this work we develop fully discrete (in time and space) numerical schemes for two-dimensional incompressible fluids ... |
Article
Conditional stability and convergence of a fully discrete scheme for three-dimensional Navier–Stokes equations with mass diffusion
(Society for Industrial and Applied Mathematics, 2008-01-01)
We construct a fully discrete numerical scheme for three-dimensional incompressible fluids with mass diffusion (in ... |
Presentation
Reproductive and time periodic solutions for incompressible fluids
(2007-09-01)
In this article, our aims is to review some of the results that are currently available concerning the existence, uniqueness ... |
Presentation
Time-periodic solutions for a generalized Boussinesq model with Neumann boundary conditions for temperature
(Royal Society of London, 2007-09-01)
The aim of this work is to prove the existence of regular time-periodic solutions for a generalized Boussinesq model (with ... |
Presentation
Regularidad anisótropa de un problema de Ecuaciones Primitivas
(2007-09-01)
En este trabajo estudiamos la regularidad de las Ecuaciones Primitivas (EP) del Océano, con condición de contorno sobre ... |
Presentation
Aproximación de un modelo de cristales líquidos nemáticos con un esquema completamente discreto y penalizado
(2007-09-01)
En esta comunicación proponemos y analizamos un esquema numérico totalmente discreto con elementos finitos en espacio y ... |
Presentation
Error estimates of optimal order in a fractional-step scheme for the 3D Navier-Stokes equations
(2007-09-01)
We present some improvements on the error estimates obtained by J.Blasco and R.Codina for a viscosity-splitting in time ... |
| Presentation |
Article
A review on reproductivity and time periodicity for incompressible fluids
(Sociedad Española de Matemática Aplicada, 2007-01-01)
In this article, our aims is to review some of the results that are currently available concerning the existence, uniqueness ... |
Article
Reproductivity for a nematic liquid crystal model
(2006-11-01)
In this paper we prove existence of weak solution with the reproductivity in time property, for a penalized PDE's system ... |
Presentation
Periodicity for a nematic liquid crystal model
(2006-08-01)
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| Presentation |
| Presentation |
Article
Local strong solution for the incompressible Korteweg model
(Elsevier, 2006-02-01)
We consider a Navier-Stokes type system with a Korteweg stress tensor, coupled with a concentration equation without ... |
| Presentation |
Article
Local and global strong solution by the semi-Galerkin method for the model of mass diffusion
(Sociedade Brasileira de Matemática, 2006-01-01)
In this work, we present some results for local and global in time solutions (defined in the time interval (0, T) with T ... |
Article
On the uniqueness and regularity of the Primitive Equations imposing additional anisotropic regularity
(Elsevier, 2005-07-01)
In this note, we prove that given u a weak solution of the Primitive Equations, imposing an additional condition on the ... |
Presentation
Regular time-reproductive solutions for generalized Boussinesq model with Neumann boundary conditions for temperature
(2005-01-01)
The aim of this work is to prove existence of regular time reproductive solutions for a generalized Boussinesq model (with ... |
Article
A review on the improved regularity for the primitive equations
(2005-01-01)
In this work we will study, some types of regularity properties of solutions for the geophysical model of hydrostatic ... |
| Article |
Article
A corrector for the Sverdrup solution for a domain with islands
(Taylor & Francis, 2004-03-01)
In this paper we look at the influence of the Coriolis force on the quasi-geostrophic equations on a domain with islands. ... |
Article
A note on a degenerate elliptic equation with applications for lakes and seas
(Texas State University, 2004-01-01)
In this paper, we give an intermediate regularity result on a degenerate elliptic equation with a weight blowing up on the ... |
Article
Density-dependent incompressible fluids with non-Newtonian viscosity
(Institute of Mathematics, Czech Academy of Sciences, 2004-01-01)
We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant ... |
Article
Hydrostatic Stokes equations with non-smooth data for mixed boundary conditions
(Elsevier, 2004-01-01)
The main subject of this work is to study the concept of very weak solution for the hydrostatic Stokes system with mixed ... |
Presentation
Optimal control and partial differential equations
(2004-01-01)
In this work, some type of optimal control problems with equality constraints given by Partial Differential Equations (PDE) ... |
Article
Asymptotic derivation of a Navier condition for the primitive equations
(IOS Press, 2003-03-01)
This paper is devoted to the establishment of a friction boundary condition associated with hydrostatic Navier-Stokes ... |
Article
On the uniqueness of weak solutions of the two-dimensional primitive equations
(Ohio University Press, 2003-01-01)
The uniqueness of weak solutions of the primitive equations with Dirichlet boundary conditions at the bottom is an open ... |
Article
Global solution of nematic liquid crystals models
(Elsevier, 2002-12-15)
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. |
Article
On the strong solutions of the primitive equations in 2D domains
(Elsevier, 2002-09-01)
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Article
Sobre la regularidad, unicidad y justificación asintótica del problema de Ecuaciones Primitivas del Océano
(Sociedad Española de Matemática Aplicada, 2002-01-01)
En este trabajo exponemos, y comentamos brevemente, los resultados obtenidos en la Tesis Doctoral de M. A. Rodríguez ... |
Article
Global in time solutions for the Poiseuille flow of Oldroyd type in 3D domains
(Springer-Verlag, 2001-12-01)
A Poiseuille flow in a 3D cylindrical domain is considered for a non-newtonian fluid of Oldroyd type. We prove existence ... |
Article
On the singular times of fluids with nonlinear viscosity
(Elsevier, 2001-11-15)
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| PhD Thesis |
Presentation
Uniqueness of solution for the 2D Primitive Equations with friction condition on the bottom
(2001-01-01)
Uniqueness of solution for the Primitive Equations with Dirichlet conditions on the bottom is an open problem even in 2D ... |
Article
Mathematical justification of the hydrostatic approximation in the primitive equations of geophysical fluid dynamics
(Society for Industrial and Applied Mathematics, 2001-01-01)
Geophysical fluids all exhibit a common feature: their aspect ratio (depth to horizontal width) is very small. This leads ... |
Article
Anisotropic estimates and strong solutions of the primitive equations
(Ohio University Press, 2001-01-01)
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PhD Thesis
Contribución al estudio teórico de algunas E.D.P. no lineales relacionadas con fluidos no newtonianos
(1995-01-01)
El objetivo básico de esta Memoria es aportar nuevos resultados teóricos de existencia, unicidad y dependencia continua ... |
PhD Thesis
Nuevos resultados sobre el problema de Navier-Stokes con densidad variable y algunas variantes: Existencia, unicidad, otros resultados teóricos y aproximación numérica
(1992-09-25)
Haremos a continuación una breve descripción de cada uno de los Capítulos de los que consta esta Memoria. Comenzamos el ... |