In this paper we investigate local and global existence as well as asymptotic behavior of the solution for a class of abstract (hyperbolic) quasilinear equations perturbed by bounded delay operators. We assume that the leading operator is of bounded variation in time. In the last section, the abstract results are applied on a heat conduction model.
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Tomáš Bárta, Delayed Quasilinear Evolution Equations with <em>BV</em>-Coefficients. Z. Anal. Anwend. 29 (2010), no. 2, pp. 149–162DOI 10.4171/ZAA/1403