Maximal subspaces for solutions of the second order abstract cauchy problem

Abstract

For a continuous, increasing function ω : R + → R + \{0} of finite exponential type, this paper introduces the set Z(A, ω) of all x in a Banach space X for which the second order abstract differential equation (2) has a mild solution such that [ω(t)] −1 u(t, x) is uniformly continues on R + , and show that Z(A, ω) is a maximal Banach subspace continuously embedded in X, where A ∈ B(X) is closed. Moreover, A| Z(A,ω) generates an O(ω(t)) strongly continuous cosine operator function family.

Research on Evaluation of Corrosion Grade Based on Image Processing Technique

“…Median filter wave will restrain the interferential impulses and punctuate yawp and will better keep the image edge's nonlinear characters [6]. There are all kinds of eliminate yawp methods used median filter wave, commonly used small dimension window and then increase the window's dimension slowly.…”