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This article proposes a new approach for computing a semi-explicit form of the solution to a class of Hamilton-Jacobi (HJ) partial differential equations (PDEs), using control techniques based on viability theory. We characterize the epigraph of the value function solving the HJ PDE as a capture basin of a target through an auxiliary dynamical system, called "characteristic system". The properties of capture basins enable us to define components as building blocks of the solution to the HJ PDEdoi:10.1109/tac.2010.2041976 fatcat:t5v2hrijpjb47dglkink5gb56q