Abstract
In this paper, the Cauchy problem for linear and nonlinear wave equations is studied. The equation involves abstract operator [Formula: see text] in a Banach space [Formula: see text] and convolution terms. Here, assuming enough smoothness on the initial data and on coefficients, the existence, uniqueness and regularity properties of local and global solutions are established in terms of fractional powers of a given sectorial operator [Formula: see text]. We obtain the regularity properties of a wide class of wave equations by choosing the space [Formula: see text] and the operator [Formula: see text] which appear in the field of physics.
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