Search results for "Strongly monotone"

An implicit non-linear time dependent equation has a solution

1991

has a solution (u, u, w). The operators &s(l) and a(t) are maximal monotone from a real Hilbert space V to its dual such that &(r) + 9?(r) are V-coercive and a(r) are not degenerate. A linear compact injection i embeds V to a real Banach space W and each d(r) is the strongly monotone subdifferential of a continuous convex function #(I, ) on W. The function f is square integrable. The functions W(r): V+ W* are Lipschitzian as V*-valued functions. Section 3 contains the theorems. The main result is Theorem 2. Theorems 3 and 4 demonstrate the smoothing effect on the initial condition. Their proofs are given in Section 4. They exploit the methods of di Benedetto and Showalter, [4], who studied …