On a local solvability of the multidimensional Muskat problem with a fractional derivative in time on the boundary condition

DOI10.7153/fdc-04-06zbMath1412.35387OpenAlexW2507190859MaRDI QIDQ4626344

Nataliya Vasylyeva

Publication date: 27 February 2019

Published in: Fractional Differential Calculus (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/fdc-04-06

zbMATH Keywords

free boundary problemanomalous diffusionCaputo derivativeMuskat problem

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Integral representations of solutions to PDEs (35C15) Free boundary problems for PDEs (35R35) Fractional partial differential equations (35R11)

Related Items

The Hele-Shaw problem with surface tension in the case of subdiffusion, Time-fractional diffusion equation with dynamical boundary condition, Solvability of a linear system with a nonlocal term in a boundary condition, Asymptotic analysis of a contact Hele-Shaw problem in a thin domain, Local solvability of a linear system with a fractional derivative in time in a boundary condition

Cites Work

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• Fractional-parabolic systems
• On a multidimensional moving boundary problem governed by anomalous diffusion: analytical and numerical study
• On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results
• An exact solution of a limit case Stefan problem governed by a fractional diffusion equation
• The Muskat problem with surface tension and a nonregular initial interface
• Classical solutions of the Stefan problem
• Fractals and fractional calculus in continuum mechanics
• On a nonclassical fractional boundary-value problem for the Laplace operator
• Some exact solutions to Stefan problems with fractional differential equations
• Linear and quasilinear elliptic equations
• Global existence, singular solutions, and ill-posedness for the Muskat problem
• The fundamental solution of a diffusion-wave equation of fractional order
• Viscous Fingering: An Optimal Bound on the Growth Rate of the Mixing Zone
• An exact solution to the moving boundary problem with fractional anomalous diffusion in drug release devices
• A note on the two-phase Hele-Shaw problem
• Well-posedness of two-phase Hele–Shaw flow without surface tension
• On one proof of the classical solvability of the Hele-Shaw problem with free boundary
• The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension
• Moving boundary problems for time fractional and composition dependent diffusion
• Moving boundary problems governed by anomalous diffusion
• Analytic semigroups and optimal regularity in parabolic problems
• Estimates for the solution of the second initial boundary-value problem for the Stokes system in the spaces of functions having Hölder continuous derivatives with respect to the spatial variables