Blow-Up in Nonlinear Equations of Mathematical Physics

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