Fredholm transformation on Laplacian and rapid stabilization for the heat equation
نویسندگان
چکیده
We study the rapid stabilization of heat equation on 1-dimensional torus using backstepping method with a Fredholm transformation. This classical framework allows us to present transformations for Laplace operator in sharp functional setting, which is main objective this work. first prove that, under some assumptions control operator, two scalar controls are necessary and sufficient get controllability stabilization. Then, we that transformation constructed Laplacian also leads local stability viscous Burgers equation.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2022
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2022.109664