THE GEOMETRIC PROPERTIES OF A DEGENERATE PARABOLIC EQUATION WITH PERIODIC SOURCE TERM

In this paper, we discuss the geometric properties of solution and lower bound estimate of Delta u(m-1) of the Cauchy problem for a degenerate parabolic equation with periodic source term u(t) = Delta u(m) + u(p) sin t. Our objective is to show that: (1) with continuous variation of time t, the surface phi = [u(x, t)](m delta/q) is a complete Riemannian manifold floating in space RN+1 and is tangent to the space R-N at partial derivative H-0(t); (2) the surface u = u(x, t) is tangent to the hyperplane W(t) at partial derivative H-u(t).