Capítulos (Ecuaciones Diferenciales y Análisis Numérico)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10835

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Asymptotic behavior of a viscous fluid near a rough boundary
(Springer, 2011) Casado Díaz, Juan; Luna Laynez, Manuel; Ecuaciones Diferenciales y Análisis Numérico; Ministerio de Ciencia e Innovación (MICIN). España; FQM309: Control y Homogeneización de Ecuaciones en Derivadas Parciales
Innovación en la enseñanza de los modelos poblacionales
(Universidad de Sevilla, 2024-01-12) Bandera Moreno, Alejandro; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
En el presente trabajo se resumen los resultados obtenidos tras la implementación de un Ciclo de Mejora en el Aula (CIMA) en la asignatura de Informática Aplicada a la Biología impartida en el primer cuatrimestre del primer año del Grado en Biología durante el curso 2023/24. En particular, el CIMA se centró en el tercer módulo de la parte de prácticas de la asignatura, que trata sobre los modelos poblacionales, tanto discretos como continuos. El principal objetivo del CIMA es mejorar la capacidad de análisis de los estudiantes para poder realizar una toma de decisiones más acertada.
Remarks on the Control of Family of b–Equations
(Elsevier, 2019) Fernández Cara, Enrique; Araujo de Souza, Diego; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Universidad de Sevilla. FQM131: Ec.diferenciales,Simulacion Num.y Desarrollo Software
Presents cutting-edge results in the areas of control theory and PDEs, giving a broad picture of recent advances Contains contributions from leading experts Includes theoretical studies and models for applications
Nonlocal elliptic system arising from the growth of cancer stem cells
(AIMS, 2018-04-18) Delgado Delgado, Manuel; Mendes Duarte, Ítalo Bruno; Suárez Fernández, Antonio; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Universidad de Sevilla. FQM131: Ec.diferenciales,Simulacion Num.y Desarrollo Software
In this work we show the existence of coexistence states for a nonlocal elliptic system arising from the growth of cancer stem cells. For this, we use the bifurcation method and the theory of the fixed point index in cones. Moreover, in some cases we study the behaviour of the coexistence region, depending on the parameters of the problem.
Multi-valued random dynamics og stochastic wave equations with infinite delays
(AIMS, 2022-10-01) Wang, Jingyu; Wang, Yejuan; Caraballo Garrido, Tomás; Universidad de Sevilla. Departamento de Ecuaciones diferenciales y Análisis numérico; Universidad de Sevilla. FQM314: Análisis Estocástico de Sistemas Diferenciales
This paper is devoted to the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with infinite delays. The nonlinear terms of the equation are not expected to be Lipschitz continuous, but only satisfy continuity assumptions along with growth conditions, under which the uniqueness of the solutions may not hold. Using the theory of multi-valued non-autonomous random dynamical systems, we prove the existence and measurability of a compact global pullback attractor.
Some aspects concerning the dynamics of stochastic chemostats
(Springer, 2016) Caraballo Garrido, Tomás; Garrido Atienza, María José; López de la Cruz, Javier; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Sadovnichiy, Victor A.; Zgurovsky, Mikhail Z.; Universidad de Sevilla. FQM314: Análisis Estocástico de Sistemas Diferenciales
In this paper we study a simple chemostat model influenced by white noise which makes this kind of models more realistic. We use the theory of random attractors and, to that end, we first perform a change of variable using the OrnsteinUhlenbeck process, transforming our stochastic model into a system of differential equations with random coefficients. After proving that this random system possesses a unique solution for any initial value, we analyze the existence of random attractors. Finally we illustrate our results with some numerical simulations.
Control of weakly blowing up semilinear heat equations
(Springer, 2002) Fernández Cara, Enrique; Zuazua Iriondo, Enrique; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Berestycki, Henri; Pomeau, Yves; Universidad de Sevilla. FQM131: Ec.diferenciales,Simulación Num.y Desarrollo Software
In these notes we consider a semilinear heat equation in a bounded domain of IRd , with control on a subdomain and homogeneous Dirichlet boundary conditions. We consider nonlinearities for which, in the absence of control, blow up arises. We prove that when the nonlinearity grows at infinity fast enough, due to the local (in space) nature of the blow up phenomena, the control may not avoid the blow up to occur for suitable initial data. This is done by means of localized energy estimates. However, we also show that when the nonlinearity is weak enough, and provided the system admits a globally defined solution (for some initial data and control), the choice of a suitable control guarantees the global existence of solutions and moreover that the solution may be driven in any finite time to the globally defined solution. In order for this to be true we require the nonlinearity f to satisfy at infinity the growth condition f(s) |s| log3/2 (1 + |s|) → 0 as |s| → ∞. This is done by means of a fixed point argument and a careful analysis of the control of linearized heat equations relying on global Carleman estimates. The problem of controlling the blow up in this sense remains open for nonlinearities growing at infinity like f(s) ∼ |s|logp (1 + |s|) with 3/2 ≤ p ≤ 2.
Some indefinite nonlinear eigenvalue problems
(World Scientific, 2004) Suárez Fernández, Antonio; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Delgado Delgado, Manuel; López Gómez, Julián; Ortega Ríos, Rafael; Suárez Fernández, Antonio; Universidad de Sevilla. FQM131: Ec.diferenciales,Simulación Num.y Desarrollo Software
In this work we study the structure of the set of positive solutions of a nonlinear eigenvalue problem with a weight changing sign. Specifically, the reaction term arises from a population dynamic model. We use mainly bifurcation methods to obtain our results.
Some elliptic problems with nonlinear boundary conditions
(World Scientific, 2005) Morales Rodrigo, Cristian; Suárez Fernández, Antonio; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Cano Casanova, Santiago; López Gómez, Julián; Mora Corral, Carlos; Universidad de Sevilla. FQM131: Ec.diferenciales,Simulación Num.y Desarrollo Software
This paper concerns with some elliptic equations with non-linear boundary conditions. Sub-supersolution and bifurcation methods are used in order to obtain existence, uniqueness or multiplicity of positive solutions.
Attracting complex networks
(Springer, 2016) Guerrero Suárez, Giovanny Fabián; Langa Rosado, José Antonio; Suárez Fernández, Antonio; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Commendatore, Pasquale; Matilla García, Mariano; Varela Cabo, Luis Miguel; Cánovas Peña, José Salvador; Universidad de Sevilla. FQM314: Análisis Estocástico de Sistemas Diferenciales
Real phenomena from different areas of Life Sciences can be described by complex networks, whose structure is usually determining their intrinsic dynamics. On the other hand, Dynamical Systems Theory is a powerful tool for the study of evolution processes in real situations. The concept of global attractor is the central one in this theory. In the last decades there has been an intensive research in the geometrical characterization of global attractors. However, there still exists a weak connection between the asymptotic dynamics of a complex network and the structure of associated global attractors. In this paper we show that, in order to analyze the long-time behavior of the dynamics on a complex network, it is the topological and geometrical structure of the attractor the subject to take into account. In fact, given a complex network, a global attractor can be understood as the new attracting complex network which is really describing and determining the forwards dynamics of the phenomena. We illustrate our discussion with models of differential equations related to mutualistic complex networks in Economy and Ecology.
Some properties on the Q-Tensor system
(Universidad de Zaragoza, 2014) Guillén González, Francisco Manuel; Rodríguez Bellido, María Ángeles; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; López de Silanes Busto, María Cruz; Palacios Latasa, Manuel Pedro; Sanz Sáiz, Gerardo; Amrouche, Chérif; Universidad de Sevilla. FQM131: Ec.diferenciales,Simulación Num.y Desarrollo Software
We study the coupled Navier-Stokes and Q-Tensor system (analyzed in cf. [Paicu, M., and Zarnescu, A. Energy dissipation and regularity for a coupled Navier-Stokes and Q-tensor system. Arch. Ration. Mech. Anal. 203 (2012), 45–67] in the whole R3) in a bounded three-dimensional domain for several boundary conditions, rewriting the system in a way that properties as symmetry and null-trace for the tensor Q can be proved. We show some analytical results such as: the existence of global in time weak solution, a maximum principle for the Q-tensor, local in time strong solution (which is global assuming an additional regularity criterion for the velocity in the space-periodic boundary condition case), global in time strong solution imposing dominant viscosity (for the space-periodic or homogeneous Neumann boundary condition cases) and regularity criteria for uniqueness of weak solutions.
Lévy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces
(Springer, 2015) Garrido Atienza, María José; Lu, Kening; Schmalfuss, Björn; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Sadovnichiy, Victor A.; Zgurovsky, Mikhail Z.; Universidad de Sevilla. FQM314: Análisis Estocástico de Sistemas Diferenciales
In this paper we investigate the existence and some useful properties of the Lévy areas of Ornstein-Uhlenbeck processes associated to Hilbert-space-valued fractional Brownian-motions with Hurst parameter H ∈ (1/3, 1/2]. We prove that this stochastic area has a Hölder-continuous version with sufficiently large Hölder-exponent and that can be approximated by smooth areas. In addition, we prove the stationarity of this area.

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