20 citations · 112 across the 42 of their papers we have counts for
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Schock waves and compactons for fifth-order nonlinear dispersion equations. II
V. A. Galaktionov
It is shown that fifth-order nonlinear dispersion equations from compacton theory admit shock and rarefaction waves. A self-similar gradient blow-up is shown to admit infinitely ma…
Branching analysis of a countable family of global similarity solutions of a fourth-order thin film equation
P. Alvarez-Caudevilla, V. A. Galaktionov
We show that various asymptotic properties of global solutions of a fourth-order quasilinear thin film equation can be described by branching from corresponding solutions of the li…
On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation I. Local oscillatory properties
M. Chaves, V. A. Galaktionov
Local oscillatory and other properties of source-type solutions of doubly nonlinear sixth-order parabolic thin film equations are studied.
Self-similar blow-up in parabolic equations of Monge--Ampère type
C. R. Budd, V. A. Galaktionov
We propose nonlinear parabolic equations of Monge--Ampére (M--A) type that admit regional, single poin, and global blow-up of similarity type. A similar model is derived for a four…
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…
On blow-up shock waves for a nonlinear PDE associated with Euler equations
V. A. Galaktionov
A second-order PDE is derived from Euler's equaitons under certain assumptions. It is shown that this PDE admits shock and rarefaction waves, and that a single point gradient blow-…