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