Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term
In this paper we study the null controllability cost of a transport-diffusion system under Robin boundary conditions with distributed control and in which the transport coefficient is a gradient field. First, we provide some conditions on transport coefficient and boundary potential to show that the...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2024 |
| País: | España |
| Recursos: | Universidad del País Vasco |
| Repositório: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/73738 |
| Acesso em linha: | http://hdl.handle.net/10810/73738 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Carleman estimates Uniform controllability Transport equation Singular limits Cost control Spectral decomposition |
| Resumo: | In this paper we study the null controllability cost of a transport-diffusion system under Robin boundary conditions with distributed control and in which the transport coefficient is a gradient field. First, we provide some conditions on transport coefficient and boundary potential to show that the control cost decays exponentially when the viscosity vanishes and the control time is sufficiently large. On the other hand, if the range of the control region by the transport flow does not cover that of $\Omega$, we prove that the control cost explodes exponentially for the Neumann boundary conditions case with vanishing viscosity and all control time. |
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