The geometric properties of a degenerate parabolic equation with periodic source term

Document Type: Research Paper


1 Institute of Mathematics‎, ‎Shanghai Normal University‎, ‎Shanghai‎, ‎200235‎, ‎China and ‎Institute of Mathematics‎, ‎Jimei University‎, ‎Xiamen‎, ‎361021 China.

2 Institute of Mathematics‎, ‎Jimei University‎, ‎Xiamen‎, ‎361021 China.


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).


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