Singular Solution Of A Quasilinear Convection Diffusion Degenerate Parabolic Equation With Absorption

In this paper we discussed the Cauchy problem where p > 2, q > 0, b_i(s)∈C~1(R).In this paper, we are interested in the existence and nonexistence of non-negative and non-trivial solution of Cauchy problem (l)with initial datau(x,0) =δ(x) x∈R~N (3)where δ(x) denotes the Dirac mass centered at the origin.We have proved that let p > 2, if 0p-1 +p/N,0≤m≤q(p+Np-N-1)/p+Np-N , then(1)(3) has no solution; if p -1 < q < p -1+ p/N, 0≤ m < q, then (1)(2) has a very singular solution, i.e. a solution ω with the following properties:ω∈C(S|-_T\{(0,0)})ω(x,0) = 0 (?)x∈R~N\{0} then (1)(2) has no very singular solution. Here we use the methods similar to that in [1].