  We explore Kapitza thermal resistance on the boundary between two homogeneous
chain fragments with different characteristics. For a linear model, an exact
expression for the resistance is derived, and well-defined in the thermodynamic
limit. However, the resistance in this case depends on the thermostat
properties and therefore is not a local property of the considered domain
boundary. If the domains are nonlinear, but integrable - Toda lattice,
elastically colliding particles - the anomalies are similar to the case of the
linear chain, besides well-articulated thermal dependence of the resistance.
For the case of elastically colliding particles, this dependence follows a
simple scaling law - the resistance is proportional to the inverse square root
of the temperature. For Fermi-Pasta-Ulam domains, both the temperature drop and
the heat flux decrease with the chain length, but with different exponents, so
the resistance vanishes in the thermodynamic limit. For the domains comprised
of rotators, the thermal resistance exhibits the expected normal behavior.
