Very singular solutions for the thin film equation with absorption
Analysis of PDEs
2009-01-27 v1
Authors:
V. A. Galaktionov
Abstract
Self-similar large time behaviour of weak solutions of the fourth-order parabolic thin film equations with absorption is studued.
Keywords
Cite
@article{arxiv.0901.3982,
title = {Very singular solutions for the thin film equation with absorption},
author = {V. A. Galaktionov},
journal= {arXiv preprint arXiv:0901.3982},
year = {2009}
}
Comments
20 pages, 13 figures
Related papers
View all related →
Analysis of PDEs · Mathematics
On Continuous Branches of Very Singular Similarity Solutions of the Stable Thin Film Equation
J. D. Evans, V. A. Galaktionov
2010-03-08
Analysis of PDEs · Mathematics
Strong solutions of the thin film equation in spherical geometry
Roman M. Taranets
2017-10-02
Analysis of PDEs · Mathematics
Weak Solution of a Doubly Degenerate Parabolic Equation
Di Kang, Tharathep Sangsawang, Jialun Zhang
2017-03-02
Analysis of PDEs · Mathematics
Self-similarity in a thin film Muskat problem
Philippe Laurencot, Bogdan-Vasile Matioc
2014-09-26
Analysis of PDEs · Mathematics
On centre subspace behaviour in thin flm equations
V. A. Galaktionov, P. J. Harwin
2009-01-27
Analysis of PDEs · Mathematics
Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations
Giulio Schimperna, Sergey Zelik
2010-09-17
Analysis of PDEs · Mathematics
Weak solutions to a thin film model with capillary effects and insoluble surfactant
Joachim Escher, Matthieu Hillairet, Philippe Laurencot, Christoph Walker
2012-12-27
Analysis of PDEs · Mathematics
Singular solutions of some nonlinear parabolic equations with spatially inhomogeneous absorption
Andrey Shishkov, Laurent Veron
2007-08-23
Analysis of PDEs · Mathematics
Long-time asymptotics and regularity estimates for weak solutions to a doubly degenerate thin-film equation in the Taylor-Couette setting
Christina Lienstromberg, Juan J. L. Velázquez
2024-02-28
Analysis of PDEs · Mathematics
Nonnegative solutions for a long-wave unstable thin film equation with convection
Marina Chugunova, M. C. Pugh, R. M. Taranets
2009-10-30
Analysis of PDEs · Mathematics
Asymptotic behavior for the fast diffusion equation with absorption and singularity
Changping Xie, Shaomei Fang, Ming Mei, Yuming Qin
2024-05-14
Analysis of PDEs · Mathematics
Invariant Manifolds for the Thin Film Equation
Christian Seis, Dominik Winkler
2022-12-06
Analysis of PDEs · Mathematics
Existence and uniqueness of very singular solutions for a fast diffusion equation with gradient absorption
Razvan Gabriel Iagar, Philippe Laurencot
2013-08-29
Analysis of PDEs · Mathematics
Weak solutions to a two-phase thin film model with insoluble surfactant driven by capillary effects
Gabriele Bruell
2016-08-30
Analysis of PDEs · Mathematics
On a nonlocal degenerate parabolic problem
Rui M. P. Almeida, Stanislav N. Antontsev, José C. M. Duque
2014-07-28
Analysis of PDEs · Mathematics
Second order asymptotics and uniqueness for self-similar profiles to a singular diffusion equation with gradient absorption
Razvan Gabriel Iagar, Philippe Laurençot
2024-06-18
Analysis of PDEs · Mathematics
The properties of the solution for the Cauchy problem of a double nonlinear time-dependent parabolic equation in non-divergence form with a source or absorption
Mersiad Aripov, Makhmud Bobokandov
2025-07-03
Analysis of PDEs · Mathematics
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
2009-11-03
Analysis of PDEs · Mathematics
Asymptotic Stability and the Forcing Term: An Analysis of Non-Newtonian Thin-Film Flows
Jinhong Zhao, Bin Guo
2026-01-06
Functional Analysis · Mathematics
Asymptotic behaviour of solutions of fourth order Dirichlet problems
Paolo Dall'Aglio
2007-05-23
Analysis of PDEs · Mathematics
Large-time behavior of compressible polytropic fluids and nonlinear Schr{\"o}dinger equation
Rémi Carles, Kleber Carrapatoso, Matthieu Hillairet
2023-12-04
Mathematical Physics · Physics
Long-time self-similar asymptotic of the macroscopic quantum models
Hai-Liang Li, Guo-Jing Zhang, Min Zhang, Chengchun Hao
2008-11-25
Analysis of PDEs · Mathematics
Branching analysis of a countable family of global similarity solutions of a fourth-order thin film equation
P. Alvarez-Caudevilla, V. A. Galaktionov
2009-11-17
Analysis of PDEs · Mathematics
Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
Zhirayr Avetisyan, Zahra Keyshams, Monire Mikaeili Nia, Michael Ruzhansky
2026-04-28
Analysis of PDEs · Mathematics
Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
Zhirayr Avetisyan, Zahra Keyshams, Monire Mikaeili Nia, Michael Ruzhansky
2025-07-22