Preprint Nonautonomous differential equations and Lipschitz evolution operators in Banach spaces

小林 良和

Description
A new class of Lipschitz evolution operators is introduced and a characterization of continuous in nitesimal generators of such evolution operators is given. It is shown that a continuous mapping A from a subset Ω of [a; b) X into X, where [a; b) is a real half-open interval and X is a real Banach space, is the in nitesimal generator of a Lipschitz evolution operator if and only if it satis es a sub-tangential condition, a general type of quasi-dissipative condition with respect to a metric-like functional and a connectedness condition. An application of the results to the initial value problem for the quasilinear wave equation with dissipation is also given.
Full-Text

http://ir.c.chuo-u.ac.jp/repository/search/binary/p/7203/s/5093/

Number of accesses :  

Other information