"In the present book a method for solving evolutionary problems is described. The outline of this method is as follows. The initial-boundary value problem is considered as an operator equation which naturally corresponds to the underlying problem. The involved operator often does not possess good properties, therefore certain approximations of this equation are considered, which result e.g. from smoothing of nonlinear terms. One then studies the solvability of this approximating equation in spaces with better topological properties. For this purpose, one applies the technique of the Leray-Schauder topological degree or its generalizations. The approximating equation has natural properties, which allows to apply various approximating methods for the analysis of this equation. The last step of the method is the passage to the limit in the approximating equation as the approximation parameters tend to zero, and here the solutions of the approximating equation converge to a solution of the original equation (usually in a weaker topology)." "In particular, this method turns out to be useful for those problems of non-Newtonian hydrodynamics where it is hard or impossible to express the deviatoric stress tensor via the velocity vector function explicitly. Here this method is used for the investigation of some models for motion of viscoelastic media. The book contains preliminary material from rheology which is required for understanding the models under consideration."--BOOK JACKET.
This volume focuses on recent developments in non-linear and hyperbolic equations. It will be a most valuable resource for researchers in applied mathematics, the theory of wavelets, and in mathematical and theoretical physics. Nine up-to-date contributions have been written on invitation by experts in the respective fields. The book is the third volume of the subseries "Advances in Partial Differential Equations".
There is an increasing demand for man-made dynamical systems to operate autonomously in the presence of faults and failures in sensors, actuators or components. Fault diagnosis and health monitoring are essential components of an autonomous system. Hence, a high demand exists for the development of intelligent systems that are able to autonomously detect the presence and isolate the location of faults occurring in different components of complex dynamical systems. Fault Diagnosis of Nonlinear Systems Using A Hybrid Approach focuses on developing a fault diagnosis methodology that enables on-line health monitoring of nonlinear systems and off-line monitoring purposes.
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