A contact geometry framework for field theories with dissipation
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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.
© 2020. Elsevier
CitationGaset, J. [et al.]. A contact geometry framework for field theories with dissipation. "Annals of physics", 1 Març 2020, vol. 414, p. 168092-1-168092-20.