Stability estimate for the semi-discrete linearized Benjamin-Bona-Mahony equation

In this work we study the semi-discrete linearized Benjamin-Bona-Mahony equation (BBM) which is a model for propagation of one-dimensional, unidirectional, small amplitude long waves in non-linear dispersive media. In particular, we derive a stability estimate which yields a unique continuation property. The proof is based on a Carleman estimate for a finite difference approximation of Laplace operator with boundary observation in which the large parameter is connected to the mesh size. Mathematics Subject Classification. 35B60, 35L05, 35Q35, 35R45, 65M06. Received November 26, 2020. Accepted August 29, 2021. Dedicated to Enrique Zuazua on the occasion of his 60th birthday

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