Inverse Problems and Control Theory.
El Seminario IPCT (por sus siglas en inglés Inverse Problems and Control Theory) es un seminario conjunto entre las universidades UChile – UC – UTFSM – USACH con inicio en Septiembre 2024, el cual tiene como objetivo reunir a una comunidad científica en torno a los temas de problemas inversos y de la teoría de control en ecuaciones diferenciales además de sus aplicaciones en diversas áreas como son la ingeniería, la biomedicina, las ciencias de la tierra y del espacio entre otras. El seminario será de carácter itinerante entre las instituciones participantes y se realizará en modalidad híbrida, presencial y con transmisión online si las condiciones técnicas en cada ocasión lo permiten.
2024-10-17
16:30hrs.
16:30hrs.
Sylvain Ervedoza. Institut de Mathématiques de Bordeaux, Université de Bordeaux and Cnrs
On the reachabe space for the heat equation
Auditorio Ninoslav Bralic, Facultad de Matemática, Universidad Católica de Chile.
Abstract:
The goal of this talk is to explain how perturbative arguments can be applied to derive a sharp description of the reachable space for heat equations having lower order terms. The main result I will present is the following one. Let us consider an abstract system y’ = Ay + Bu, where A is an operator generating a C0 semigroup (exp(tA))t≥0 on a Hilbert space X, and B is a control operator, for instance a linear operator from an Hilbert space U to X, and let us assume that this system is null-controllable in X in any positive time. Then, setting R the reachable set of the system (that is all the states that can be achieved by y solution of y’ = Ay + Bu, y(0) = 0), the restriction of (exp(tA))t≥0 to R forms a C0 semigroup on R. Accordingly, the system y’ = Ay + Bu is exactly controllable on R, and one can then perform classical perturbative arguments to handle lower order terms, as I will explain on a few examples. This talk is based on a joint work with Kévin Le Balc’h (INRIA Paris) and Marius Tucsnak (Bordeaux). If time allows, I will also explain the strategy we develop in a recent work with Adrien Tendani-Soler (Bordeaux) to get a more refined description of the reachable space in the case of a ball controlled from its entire boundary, following the recent approach by Alexander Strohmaier and Alden Waters.
https://eventos.cmm.uchile.cl/seminarioipct/
On the reachabe space for the heat equation
Auditorio Ninoslav Bralic, Facultad de Matemática, Universidad Católica de Chile.
Abstract:
The goal of this talk is to explain how perturbative arguments can be applied to derive a sharp description of the reachable space for heat equations having lower order terms. The main result I will present is the following one. Let us consider an abstract system y’ = Ay + Bu, where A is an operator generating a C0 semigroup (exp(tA))t≥0 on a Hilbert space X, and B is a control operator, for instance a linear operator from an Hilbert space U to X, and let us assume that this system is null-controllable in X in any positive time. Then, setting R the reachable set of the system (that is all the states that can be achieved by y solution of y’ = Ay + Bu, y(0) = 0), the restriction of (exp(tA))t≥0 to R forms a C0 semigroup on R. Accordingly, the system y’ = Ay + Bu is exactly controllable on R, and one can then perform classical perturbative arguments to handle lower order terms, as I will explain on a few examples. This talk is based on a joint work with Kévin Le Balc’h (INRIA Paris) and Marius Tucsnak (Bordeaux). If time allows, I will also explain the strategy we develop in a recent work with Adrien Tendani-Soler (Bordeaux) to get a more refined description of the reachable space in the case of a ball controlled from its entire boundary, following the recent approach by Alexander Strohmaier and Alden Waters.
https://eventos.cmm.uchile.cl/seminarioipct/
2024-09-06
16:00hrs.
16:00hrs.
Eduardo Cerpa. Instituto de Ingeniería Matemática y Computacional, Facultad de Matemáticas, Pontificia Universidad Católica de Chile
Singular perturbation method for stability of infinite-dimensional systems
Sala de Seminarios Felipe Álvarez, Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile.
Abstract:
Coupled systems appear everywhere in complex models and in some cases there are different time scales involved. The coupling and the scales make this kind of system very difficult to study from theoretical and computational viewpoints. One hopes that some particular properties of the system could be studied through simpler uncoupled systems. This is what the singular perturbation method (SPM) does concerning stability properties. The SPM approach has been introduced for ordinary differential equations and can also be applied for partial differential equations but in the latter case there are no general theorems and stability properties have to be obtained for each particular system. In this talk we introduce the SPM for infinite-dimensional systems and obtain stability results. We will consider parabolic, hyperbolic and dispersive equations appearing in coupled systems in some cases also involving ordinary differential equations.
Singular perturbation method for stability of infinite-dimensional systems
Sala de Seminarios Felipe Álvarez, Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile.
Abstract:
Coupled systems appear everywhere in complex models and in some cases there are different time scales involved. The coupling and the scales make this kind of system very difficult to study from theoretical and computational viewpoints. One hopes that some particular properties of the system could be studied through simpler uncoupled systems. This is what the singular perturbation method (SPM) does concerning stability properties. The SPM approach has been introduced for ordinary differential equations and can also be applied for partial differential equations but in the latter case there are no general theorems and stability properties have to be obtained for each particular system. In this talk we introduce the SPM for infinite-dimensional systems and obtain stability results. We will consider parabolic, hyperbolic and dispersive equations appearing in coupled systems in some cases also involving ordinary differential equations.
Contáctenos
Edificio Rolando Chuaqui, Campus San Joaquín. Avda. Vicuña Mackenna 4860, Macul, Chile.Teléfono (+56) 95504 4511.
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