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arXiv · 1905.07354

A contact geometry framework for field theories with dissipation

Jordi Gaset·Xavier Gràcia·Miguel C. Muñoz-Lecanda·Xavier Rivas·Narciso Román-Roy
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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.

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Jordi Gaset, Xavier Gràcia, Miguel C. Muñoz-Lecanda, Xavier Rivas, Narciso Román-Roy. 2020-02-23. A contact geometry framework for field theories with dissipation. https://doi.org/10.1016/j.aop.2020.168092

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