Korpusov M.O., Ovchinnikov A.V., Sveshnikov A.G., Yushkov E.V. Blow-Up in Nonlinear Equations of Mathematical Physics: Theory and Methods

Berlin: De Gruyter, 2018. — 348 p. — (De Gruyter Series in Nonlinear Analysis and Applications, 27). — ISBN: 3110601087.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.Notation.
List of nonlinear equations.
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 Schrodinger equation.
Variational method of L. E. Payne and D. H. Sattinger.
Breaking of solutions of wave equations.
A Auxiliary and additional results.True PDF