The nonlinear version is now available as
Monotone Operators in Banach Space and Nonlinear Partial Differential Equations.
It is published in the series
Mathematical Surveys and Monographs
by the American Mathematical Society, Providence, 1997.
The 1976 monograph SINGULAR
and DEGENERATE CAUCHY PROBLEMS. with Robert
Wayne Carroll is long out of print but contains many references to
the classical literature of pseudo-parabolic equations or partial
differential equations of Sobolev-type. (See Chapter 3.)
"Applied Mathematics is not a subject classification. It's an
attitude."