the geometric properties of a degenerate parabolic equation with periodic source term
چکیده
in this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete riemannian manifold floating in space rn+1and is tangent to the space rn at ∂h0(t); (2)the surface u = u(x,t) is tangent to the hyperplane w(t) at ∂hu(t).