  In previous papers, a geometric framework has been developed to describe
non-conservative field theories as a kind of modified Lagrangian and
Hamiltonian field theories. This approach is that of $k$-contact Hamiltonian
systems, which is based on the $k$-symplectic formulation of field theories as
well as on contact geometry. In this work we present the Skinner--Rusk unified
setting for these kinds of theories, which encompasses both the Lagrangian and
Hamiltonian formalisms into a single picture. This unified framework is
specially useful when dealing with singular systems, since: (i) it incorporates
in a natural way the second-order condition for the solutions of field
equations, (ii) it allows to implement the Lagrangian and Hamiltonian
constraint algorithms in a unique simple way, and (iii) it gives the Legendre
transformation, so that the Lagrangian and the Hamiltonian formalisms are
obtained straightforwardly. We apply this description to several interesting
physical examples: the damped vibrating string, the telegrapher's equations,
and Maxwell's equations with dissipation terms.
