The Muskat problem with surface tension and a nonregular initial interface

DOI10.1016/j.na.2011.05.087zbMath1225.35258OpenAlexW2030787652MaRDI QIDQ640133

Borys V. Bazaliy, Nataliya Vasylyeva

Publication date: 17 October 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.05.087

zbMATH Keywords

surface tensionwaiting timeLaplace equationfree boundary problemsweighted Hölder spacesMuskat problem

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Free boundary problems for PDEs (35R35)

Related Items

On the Muskat problem ⋮ On a class of functional difference equations: explicit solutions, asymptotic behavior and applications ⋮ A new reformulation of the Muskat problem with surface tension ⋮ On the solvability of a transmission problem for the Laplace operator with a dynamic boundary condition on a nonregular interface ⋮ On a local solvability of the multidimensional Muskat problem with a fractional derivative in time on the boundary condition ⋮ The Muskat problem with surface tension and equal viscosities in subcritical \(L_p\)-Sobolev spaces ⋮ Self-similar solutions for the Muskat equation

Cites Work

• The Hele--Shaw problem and area-preserving curve-shortening motions
• The transmission problem in domains with a corner point for the Laplace operator in weighted Hölder spaces
• Classical solutions of the Stefan problem
• Classical solutions for Hele-Shaw models with surface tension
• Global classical solution of Muskat free boundary problem.
• The Hele-Shaw problem with surface tension in a half-plane: a model problem
• The Hele-Shaw problem with surface tension in a half-plane
• Global existence, singular solutions, and ill-posedness for the Muskat problem
• Existence results for Hele–Shaw flow driven by surface tension
• Well-posedness of two-phase Hele–Shaw flow without surface tension
• A Free Boundary Problem for an Elliptic–Parabolic System: Application to a Model of Tumor Growth
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item