A new geometric framework is developed to describe non-conservative classical
field theories, which is based on multisymplectic and contact geometries.
Assuming certain additional conditions and using the forms that define this
multicontact structure, as well as other geometric elements that are derived
from them, we can introduce variational field equations in the multicontact
manifolds. These equations are stated using different geometric tools; namely,
sections, multivector fields and Ehresmann connections in fiber bundles. Then,
this framework can be adapted to the jet bundle description of classical field
theories and the field equations are stated both in the Lagrangian and the
Hamiltonian formalisms, which are discussed in the regular and the singular
cases.
