Nonautonomous differential equations and Lipschitz evolution operators in Banach spaces

作者：Kobayashi Yoshikazu^*; Tanaka Naoki; Tomizawa Yukino

来源：Hiroshima Mathematical Journal, 2015, 45(3): 267-307.

DOI：10.32917/hmj/1448323767

• Lipschitz evolution operator
• infinitesimal generator
• sub-tangential condition
• quasi-dissipative condition
• metric-like functional
• connectedness condition

A new class of Lipschitz evolution operators is introduced and a characterization of continuous infinitesimal generators of such evolution operators is given. It is shown that a continuous mapping A from a subset Omega of [a, b) x X into X, where [a, b) is a real half-open interval and X is a real Banach space, is the infinitesimal generator of a Lipschitz evolution operator if and only if it satisfies 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.

• 出版日期2015-11