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

Abstract

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 of the system in a suitable Banach space. The second one is regarded to 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 $b-$; Fornberg-Whitham; potential and $\pi -$Camassa-Holm; generalised Boussinesq equations; and the modified Euler-Poisson system.

New section added (section 5), moderate revision carried out, and some references included

References in corpus (5)

• A New Integrable Equation with Peakon Solutions
• Conserved quantities, continuation and compactly supported solutions of some shallow water models
• Existence, continuation, persistence and dynamics of solutions for a generalized 0-Holm-Staley equation
• Geometrical demonstration for persistence properties for a bi-Hamiltonian shallow water system
• The Cauchy problem and continuation of periodic solutions for a generalized Camassa-Holm equation