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The Cauchy problem of some nonlinear doubly degenerate parabolic equations. (Chinese) Zbl 0828.35071

The authors consider the problem:

u t =div| u m | p-2 u m ,inS T = N ×(0,T),u(x,0)=u 0 (x),x N ,(1)

where p>1, m>0, u 0 0. They study the existence and uniqueness and the long-time behavior of the solution of (1). The main result is as follows: Let u and v be two solutions with initial conditions u 0 and v 0 (u 0 ,v 0 L 1 ( N )), then

N u ( x , t ) - v ( x , t )dx N u 0 (x) - v 0 (x)dx

holds.

MSC:
35K65Parabolic equations of degenerate type
35K15Second order parabolic equations, initial value problems
35B40Asymptotic behavior of solutions of PDE