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arXiv · 1611.04111

Null Controllability of the Kuramoto-Sivashinsky Equation on star-shaped trees

Cristian M. Cazacu·Liviu I. Ignat·Ademir F. Pazoto
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Abstract

In this paper we treat controllability properties for the linear Kuramoto-Sivashinsky equation on a network with two types of boundary conditions. More precisely, the equation is considered on a star-shaped tree with Dirichlet and Neumann boundary conditions. By using the moment theory we can derive null-controllability properties with boundary controls acting on the external vertices of the tree. In particular, the controllability holds if the anti-diffusion parameter of the involved equation does not belong to a critical countable set of real numbers. We point out that the critical set for which the null-controllability fails differs from the first model to the second one.

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Cristian M. Cazacu, Liviu I. Ignat, Ademir F. Pazoto. 2016-11-13. Null Controllability of the Kuramoto-Sivashinsky Equation on star-shaped trees. https://arxiv.org/abs/1611.04111

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