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7 papers · 2 filters
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.
Incomplete self-similar blow-up in a semilinear fourth-order reaction-diffusion equation
V. A. Galaktionov
It is shown that self-similar blow-up for a fourth-order reaction-diffusion equation is incomplete in the sense that, in general, there exists a self-similar extension of solutions…
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…
Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach
V. A. Galaktionov
Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type $$ u_t= -Δ^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (…
On nonexistence of Baras--Goldstein type for higher-order parabolic equations with singular potentials
V. A. Galaktionov, I. V. Kamotski
An analogy of nonexistence result by Baras and Goldstein (1984), for the heat equation with inverse singular potential, is proved for 2mth-order linear parabolic equations with Har…