Non-Homogeneous Boundary Value Problems and Applications: Volume III
Dec 2012 · Grundlehren der mathematischen Wissenschaften Book 183 · Springer Science & Business Media
Ebook
310
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About this ebook
In this second volume, we continue at first the study of nonhomogeneous boundary value problems for particular classes of evolution equations. In Chapter 4, we study parabolic operators by the method of Agranovitch-Vishik. This is step (i) 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 the sense 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-posed problems for the operators in question, is given in the Appendix. Still other applications, for example to numerical analysis, will be given in Volume 3.
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