Unique continuation results for abstract quasi-linear evolution equations in Banach spaces

. Unique continuation properties for a class of evolution equations defined on Banach spaces are considered from two different point of views: the first one is based on the existence of conserved quantities, which very often translates into the conservation of some norm of the solutions in a suitable Banach space. The second one considers well-posed problems. Our results are then applied to some equations, most of them describing physical processes like wave propagation, hydrodynamics, and integrable systems, such as the potential and pi-Camassa-Holm; generalised Boussinesq equations; and the modified Euler-Poisson system.