This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in partial differential equations and mathematical physics.

Readership

Researchers and graduate students working in partial differential equations and mathematical physics.

Table of Contents

• D. E. Apushkinskaya and A. I. Nazarov -- Hölder estimates of solutions to initial-boundary value problems for parabolic equations of nondivergent form with Wentzel boundary condition
• A. A. Arkhipova -- Reverse Hölder inequalities with boundary integrals and $L_p$-estimates for solutions of nonlinear elliptic and parabolic boundary-value problems
• Ya. Belopol'skaya -- Quasilinear parabolic equations with small parameter in a Hilbert space
• V. S. Buslaev and G. S. Perelman -- On the stability of solitary waves for nonlinear Schrödinger equations
• O. Ladyzhenskaya and G. Seregin -- On semigroups generated by initial-boundary value problems describing two-dimensional visco-plastic flows
• V. A. Malyshev -- Elliptic differential inequalities, embedding theorems, and variational problems
• V. I. Oliker and N. N. Uraltseva -- Long time behavior of flows moving by mean curvature
• V. G. Osmolovskiĭ and A. V. Sidorov -- Bifurcation problem for nonlinear second order equations in variable regions
• S. Repin and G. Seregin -- Existence of a weak solution of the minimax problem arising in Coulomb-Mohr plasticity