This book is the first attempt to develop systematically a general
theory of the initial-boundary value problems for nonlinear
evolution equations with pseudodifferential operators Ku on a
half-line or on a segment. We study traditionally important
problems, such as local and global existence of solutions and their
properties, in particular much attention is drawn to the asymptotic
behavior of solutions for large time. Up to now the theory of
nonlinear initial-boundary value problems with a general
pseudodifferential operator has not been well developed due to its
difficulty. There are many open natural questions. Firstly how many
boundary data should we pose on the initial-boundary value problems
for its correct solvability? As far as we know there are few
results in the case of nonlinear nonlocal equations. The methods
developed in this book are applicable to a wide class of dispersive
and dissipative nonlinear equations, both local and nonlocal.
-For the first time the definition of pseudodifferential operator
on a half-line and a segment is done
-A wide class of nonlinear nonlocal and local equations is
considered
-Developed theory is general and applicable to different
equations
-The book is written clearly, many examples are considered
-Asymptotic formulas can be used for numerical computations by
engineers and physicists
-The authors are recognized experts in the nonlinear wave phenomena
General
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