16 citations · 26 across the 4 of their papers we have counts for
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Variational approach to complicated similarity solutions pf higher-order nonlinear PDEs. I
V. A. Galaktionov, E. Mitidieri, S. I. Pohozaev
Three classes of higher-order nonlinear parabolic hyperbolic, and nonlinear dispersion equations are shown to admit exact blow-up or compacton solutions, which are induced by ellip…
On convergence in smooth gradient systems with branching of equilibria
V. A. Galaktionov, S. I. Pohozaev, A. E. Shishkov
T.I. Zelenyak's ideas and method of 1968 are shown to apply to N-dimensional second- and higher-order parabolic equtions and ensure a fast exponential convergence to degenerate equ…
On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations
V. A. Galaktionov, E. Mitidieri, S. I. Pohozaev
The initial boundary-value problem (IBVP) and the Cauchy problem for the Kuramoto--Sivashinsky equation and other related th-order semilinear parabolic partial differential equ…
Third-order nonlinear dispersion PDEs: shocks, rarefaction, and blow-up waves
V. A. Galaktionov, S. I. Pohozaev
Various shock and rarefaction-type similarity solutions of the third-order nonlinear dispersion equation in 1D are constructed. Blow-up of some solutions are proved by different te…