Evolution inclusions and variation inequalities for Earth data Processing. I. Operator inclusions and variation inequalities for earth data processing.
In the investigation of various mathematical models describing transient states of systems, there often appear situations when the model includes ordinary or partial differential equations with discontinuous or multivalued functions. There arises the problem of developing a theoretical apparatus for the constructive and systems analysis of such mathematical objects as differential operator inclusions and hemivariational inequalities. This problem requires the study of new classes of multivalued maps of monotone type, the verification of new methods for the search for approximate solutions, and many other topics. The book under review is devoted to the analysis of these problems. The monograph consists of two volumes. The first volume contains the systematic investigation of various classes of monotone type operators and the application of the obtained results to the study of boundary value problems with non-smooth and non-coercive interaction function and stationary variational inequalities. The contents of the first volume are the following. Chapter 1. Preliminary results. 1.1. The main results from multivalued mappings theory. 1.2. Classes of multivalued maps. 1.3. Subdifferentials in infinite-dimensional spaces. 1.4. Minimax inequalities in finite-dimensional spaces. Chapter 2. Operator inclusions and variational inequalities in infinite-dimensional spaces. 2.1. Strong solutions for parametrized operator inclusions. 2.2. Parametrized operator inequalities. 2.3. Variational inequalities in Banach and Frechet spaces. 2.4. The penalty method for multivariational inequalities. 2.5. Nonlinear operator equations of the Hammerstein type. Systems of operators equations. 2.6. Nonlinear non-coercive operator equations and their normalization. 2.7. Some examples connected with membranes theory. [For Part II, see Zbl 1213.47002.]
scientific article; zbMATH DE number 5768423