  This paper provides a new geometric framework to describe non-conservative
field theories with explicit dependence on the space-time coordinates by
combining the k-cosymplectic and k-contact formulations. This geometric
framework, the k-cocontact geometry, permits to develop a Hamiltonian and
Lagrangian formalisms for these field theories. We also compare this new
formulation in the autonomous case with the previous k-contact formalism. To
illustrate the theory, we study the nonlinear damped wave equation with
external time-dependent forcing.
