دانلود کتاب Non-Homogeneous Boundary Value Problems and Applications: Vol. 2

1. In this second volume, we continue at first the study of non-
homogeneous boundary value problems for particular classes of evolu-
tion equations.
In Chapter 4 1 , we study parabolic operators by the method of
Agranovitch- Vishik [IJ; this is step (i) (Introduction to Volume I,
Section 4), i.e. the study of regularity. The next steps: (ii) transposition,
(iii) interpolation, are similar in principle to those of Chapter 2, but
involve rather considerable additional technical difficulties.
In Chapter 5, we study hyperbolic operators or operators well-
defined in thesense of Petrowski or Schroedinger. Our regularity results
(step (i)) seem to be new. Steps (ii) and (iii) are analogous to those of
the parabolic case, except for certain technical differences.
In Chapter 6, the results of Chapters 4 and 5 are applied to the
study of optimal control problems for systems governed by evolution
equations, when the control appears in the boundary conditions (so that
non-homogeneous boundary value problems are the basic tool of this
theory). Another type of application, to the characterization of "all"
well-PQsed problems for the operators in question, is given in the Ap-
pendix. Still other applications, for example to numerical analysis, will
be: given in Volume 3.
2. For the same systems {P, Qj}, Volume 3 will proceed in an anal-
ogous way, but starting from regularity results in real analytic or
Gevrey classes. In this way, we shall be able to reach the case in which
the data t, gj are Gevrey functionals or analytic functionals.
3. The organization of the chapters is the same as for Volume 1.
In particular, the open problems are assembled in the last section of
each chapter.