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A. Khoutaibi

Publications and source records attributed to A. Khoutaibi.

2 recordsLinked to original sources
arXiv2022

Boundary null controllability for the heat equation with dynamic boundary conditions

In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control supported on an arbitrary subboundary. The proof of the main result combines a new boundary Carleman estimate and some regularity estimates for the adjoint system, with an explicit dependence with respect to the final time. This technique allows us to overcome a new difficulty that arises when absorbing a normal derivative term.

math.AP↗
arXiv2021

Parabolic equations with dynamic boundary conditions and drift terms

The aim of this paper is to study the wellposedness and $L^2$-regularity, firstly for a linear heat equation with dynamic boundary conditions by using the approach of sesquilinear forms, and secondly for its backward adjoint equation using the Galerkin approximation and the extension semigroup to a negative Sobolev space.

math.AP↗