Abstract
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.
Citation
Yoshikazu Kobayashi. Naoki Tanaka. Yukino Tomizawa. "Nonautonomous differential equations and Lipschitz evolution operators in Banach spaces." Hiroshima Math. J. 45 (3) 267 - 307, November 2015. https://doi.org/10.32917/hmj/1448323767
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