The evolution of the Local Interstellar Medium (LISM) is investigated.
The processes of interaction of the supernova remnant Loop I (North P
olar Spur) with the Local Cloud, the Sancini-van Woerden Fibre, the ba
ckground gas of the Local Cavern, and the Local Cavern envelope are co
nsidered taking into account the dynamical effects (shock wave propaga
tion) as well as the effects of thermal non-equilibrium between the el
ectron and ion gases, thermal conduction, radiation and evaporation of
dense and cold layers. It is shown that in the process of the evoluti
on of the LISM the Local Cloud can be evaporated as a result of its in
teraction with Loop I. The interaction of Loop I with the Sancini-van
Woerden Fibre can result in the evaporation of significant part of the
Fibre that can substantially influence the position of the heliopause
in the Solar System. The interaction of Loop I with the envelope of t
he Local Cavern can lead to substantial (several times) increase of th
e velocity of the envelope in comparison with the present value of its
velocity and to radiation from this region of the envelope with a tot
al intensity higher than the total luminosity of the Sun. The effect o
f saturation of thermal conduction in the process of the supernova rem
nant evolution in the low density media is discussed.