Control of hyperbolic and parabolic equations on networks and singular limits
We study the controllability properties of transport equations and of parabolic equations with vanishing diffusivity posed on a tree-shaped network. Using a control localized on the exterior nodes, we obtain a null-controllability result for both systems. The hyperbolic proof relies on the method of...
| Autores: | , , , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/73759 |
| Acceso en línea: | http://hdl.handle.net/10810/73759 |
| Access Level: | acceso abierto |
| Palabra clave: | Controllability Cost of controllability Advection-diffusion equations Vanishing viscosity Networks |
| Sumario: | We study the controllability properties of transport equations and of parabolic equations with vanishing diffusivity posed on a tree-shaped network. Using a control localized on the exterior nodes, we obtain a null-controllability result for both systems. The hyperbolic proof relies on the method of characteristics; while the parabolic one on duality arguments and Carleman inequalities. In particular, we estimate the cost of the null-controllability of advection-diffusion equations with diffusivity ε > 0 and study its asymptotic behavior when ε → 0+. More specifically, we show that the cost of null-controllability decays exponentially for a time sufficiently large and explodes for short times. The core of the proof consists in proving an observability estimate keeping track of the viscosity parameter by relying on a suitable Carleman inequality. |
|---|