16 citations · 30 across the 9 of their papers we have counts for
9 papers
Three tupes of self-similar blow-up for the fourth-order p-Laplacian equaiton with source: variational and branching approaches
V. A. Galaktionov
The fourth-order quasilinear reaction-diffusion equation with a p-Laplacian operator is shown to admit three types of blow-up. Self-similar patterns are first constructed for the r…
Formation of shocks in higher-order nonlinear dispersion PDEs: nonuniqueness and nonexistence of entropy
V. A. Galaktionov
It is shown that third-order 1D nonlinear dispersion equations admit single point gradient catastrophe, described by blow-up-type similarity solutions. After blow-up, the solutions…
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 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…
Blow-up in higher-order reaction-diffusion and wave equations: how factor occurs
V. A. Galaktionov
The origin of non self-similar blow-up in higher-order reaction-diffusion (parabolic), wave (hyperbolic) and nonlinear dispersion equations is explained by a combination of various…
Vast multiplicity of very singular self-similar solutions of a semilinear higher-order diffusion equation with time-dependent absorption
V. A. Galaktionov
It is shown that a fourth-order semilinear parabolic equation with time-dependent absorption admit a vast multiplicity of the so-called very singular self-similar solutions (VSSs),…