The objectives of this monograph are to present some topics
from the theory of monotone operators and nonlinear semigroup theory
which are directly applicable to the existence and uniqueness theory
of initial-boundary-value problems for partial differential equations
and to construct such operators as realizations of those problems in
appropriate function spaces.
A highlight of this presentation is the large number and variety of
examples introduced to illustrate the connection between the theory of
nonlinear operators and partial differential equations. These include
primarily semilinear or quasilinear equations of elliptic or of
parabolic type, degenerate cases with change of type, related systems
and variational inequalities, and spatial boundary conditions of the
usual Dirichlet, Neumann, Robin or dynamic type.
The discussions of evolution equations include the usual
initial-value problems as well as periodic or more general nonlocal
constraints, history-value problems, those which may change type due
to a possibly vanishing coefficient of the time derivative, and other
implicit evolution equations or systems including hysteresis models.
The scalar conservation law and semilinear wave equations are briefly
mentioned, and hyperbolic systems arising from vibrations of
elastic-plastic rods are developed. The origins of a representative
sample of such problems are given in the appendix.
Readership
Advanced graduate students, research mathematicians, and
engineers interested in numerical analysis, applied mathematics,
control theory, or dynamical systems.
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