A contact geometry framework for field theories with dissipation

Abstract We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of k -contact structure and k -contact Hamiltonian system. This is a generalization of both the contact Hamiltonian systems in mechanics and the k -symplectic Hamiltonian systems in field theory. The concepts of symmetries and dissipation laws are introduced and developed. Two relevant examples are analyzed in detail: the damped vibrating string and Burgers’ equation.