A NONEXISTENCE RESULT FOR DEGENERATE PARABOLIC EQUATIONS INVOLVING ADVECTION TERMS AND WEIGHTS

Abstract

In this paper, we are concerned with the following equation vt − Δλv + ∇λw · ∇λv = h(x)vp (x, t) ∈ RN × R. Here, p is a real number, w is a smooth function, h ≥ 0 is a weight function which is continuous function satisfying some growth condition at infinity, Δλ is a sub-elliptic operator which is defined by Δλ = XN i=1 ∂xi (λ2i ∂xi ) and ∇λ is the corresponding gradient operator associated to Δλ. By using a kind of maximum principle and the test function method, we establish the nonexistence of positive supersolutions of the above equation.