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The authors present functional analytical methods for solving a class of partial differential equations. The results have important applications to the numerical treatment of rheology (specific examples are the behaviour of blood or print colours) and to other applications in fluid mechanics. A class of methods for solving problems in hydrodynamics is presented.
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"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, w...
The present book carefully studies the blow-up phenomenon of solutions to partial differential equations, including many equations of mathematical physics. The included material is based on lectures read by the authors at the Lomonosov Moscow State University, and the book is addressed to a wide range of researchers and graduate students working in nonlinear partial differential equations, nonlinear functional analysis, and mathematical physics. Contents Nonlinear capacity method of S. I. Pokhozhaev Method of self-similar solutions of V. A. Galaktionov Method of test functions in combination with method of nonlinear capacity Energy method of H. A. Levine Energy method of G. Todorova Energy method of S. I. Pokhozhaev Energy method of V. K. Kalantarov and O. A. Ladyzhenskaya Energy method of M. O. Korpusov and A. G. Sveshnikov Nonlinear Schrödinger equation Variational method of L. E. Payne and D. H. Sattinger Breaking of solutions of wave equations Auxiliary and additional results
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Electron paramagnetic resonance (EPR) applications remain highly significant in modern analytical science and this volume compiles critical coverage of developments in the recent literature by a handpicked group of researchers at the cutting-edge of the field.