  The luminosity evolution of stars with highly condensed cores surrounded by
nuclear-burning shell(s) is analytically investigated with the aid of homology
relations. With respect to earlier works using a similar approach (e.g. Refsdal
& Weigert 1970; Kippenhahn 1981), the major improvement is that we derive all
the basic dependences (i.e. on core mass, core radius, and chemical
composition) in a completely generalised fashion, then accounting for a large
range of possible physical properties characterising the burning shell(s).
Parameterised formulas for the luminosity are given as a function of the (i)
relative contribution of the gas to the total pressure (gas plus radiation),
(ii) opacity source, and (iii) dominant nuclear reaction rates. In this way,
the same formalism can be applied to shell-burning stars of various
metallicities and in different evolutionary phases. In particular, we present
some applications concerning the luminosity evolution of RGB and AGB stars with
different chemical compositions, including the case of initial zero
metallicity. It turns out that homology predictions provide a good
approximation to the results of stellar model calculations. Therefore, the
proposed formalism is useful to understand the possible differences in the
luminosity evolution of shell-burning stars within a unified interpretative
framework, and can be as well adopted to improve the analytical description of
stellar properties in synthetic models.
