Global existence and L∞ estimates of solution for doubly nonlinear parabolic equation

The existence, uniqueness, and L-infinity estimate of the weak solution to the initial boundary value problem for the doubly nonlinear parabolic equation u(t) - div(\ u \(r)\del u \(m-2) del u) + del A(u) = f(x, t, u) in Omega X (0, infinity) with zero boundary condition in a bounded domain Omega subset of R-N are established. In particular, the behavior of the solution as t --> 0(+) and t --> + infinity is investigated. (C) 2000 Academic Press.