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We use the backstepping method to study the stabilization of a 1-D lineartransport equation on the interval (0, L), by controlling the scalar amplitudeof a piecewise regular function of the space variable in the source term. Weprove that if the system is controllable in a periodic Sobolev space of ordergreater than 1, then the system can be stabilized exponentially in that spaceand, for any given decay rate, we give an explicit feedback law that achievesthat decay rate.

Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback