Singular solutions of doubly singular parabolic equations with absorption

In this paper we study a doubly singular parabolic equation with absorption, ut=div(jru m j p 2 ru m ) u q with m> 0, p> 1, m(p 1) 1. We give a complete classication of solutions, which we call singular, that are non-negative, non-trivial, continuous in R n [0;1)nf(0;0)g, and satisfy u(x;0) = 0 for all x 6 0. Applications of similar but simpler equations show that thesesolutionsareveryimportantinthestudyofintermediateasymptotic behavior of general solutions.