372 citations
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5 papers · 2 filters
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…
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…
On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach
V. A. Galaktionov
It is shown that, for the bi-harmonic equation, an optimal regularity criterion of the vertex of typical paraboloids can be expressed in terms of Osgood-Dini integral conditions of…