Abstract: In the present paper the authors prove that all the generalized entropy solutions of the CJmodel, which for the given Riemann initial data are a oneparameter family u^η characterised by weak detonation discontinuity point η, are just the limits of the admissible solutions u_ek of the selfsimilar combustion model. In fact, the authors prove that for any possible η, there exists a constant B>0 s.t.
u^η=lim_{εk-e,e→0⁺,k→+m} u_εk