日時: 2026年5月18日(月) 16:30-17:15, 17:30-18:15
場所: 京都教育大学 1A402教室 (Zoom同時配信)
講演者:
16:30-17:15
講演者: Kei Fong Lam氏 (Hong Kong Baptist University)
題目: Introduction to optimal control with partial differential equations
Partial differential equations (PDEs) are mathematical descriptions of many natural and artificial real-world phenomena using equations or systems of equations involving partial derivatives of one or many variables. Much of modern research has focused primarily on demonstrating these models are well-posed and exhibit the expected qualitative behaviour. For engineering applications, we often like to steer the solution to a given/targeted state by means of control variables that will influence the state of the solution. The optimality of such a control depends on the associated cost functional. The framework of PDE constrained optimisation enables us to rigorously provide the necessary equations to compute these optimal controls. In this talk I will lay out the basics behind this framework and provide some concrete examples.
17:30-18:15
講演者: Kei Fong Lam氏 (Hong Kong Baptist University)
題目: On a PDE-ODE spatial-network model with anisotropic diffusion and metric graph structures: Well-posedness and finite-time extinction
Mathematical modeling of diffusion processes on metric graphs arises in various contexts where spatial interactions span continuous subdomains, edges, and vertices. Interactions occur and evolve within different topological structures, creating analytical challenges. Meanwhile, in practical scenarios, ranging from epidemic dynamics to chemical transport in fractured media, an effective framework to describe such dynamics is critical. In this talk, we analyze a coupled PDE-ODE defined on a hybrid structure. The model is formulated as a nonlinear system with junction conditions that capture (anisotropic) diffusion in subdomains, along edges, and coupling with well-mixed dynamics at vertices. The well-posedness of the system and qualitative properties such as regularity, boundedness and finite-time extinction will be explored. The resulting framework not only deepens the theoretical understanding of a coupled PDE-ODE model describing diffusion dynamics but also lays the groundwork for future studies on optimal control problems relevant in epidemiological and ecological settings.