Abstract

We consider initial value problems for a number of hyperbolic equations with a power-law degeneracy and with operator coefficients in a Banach space and establish sufficient conditions for the unique solvability of these problems in terms of the coefficients of the equation, the degeneracy order, and the initial elements.

中文翻译：

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具有无界算子系数的简并双曲型微分方程的可解性

摘要

我们考虑在Banach空间中具有幂律简并性和算子系数的许多双曲方程的初值问题，并根据方程的系数，简并阶数和初始元素。