Uniqueness and existence results on the Hele-Shaw and the Stefan problems
From MaRDI portal
Publication:1417399
DOI10.1007/s00205-003-0251-zzbMath1044.76019OpenAlexW2084406624MaRDI QIDQ1417399
Publication date: 5 January 2004
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00205-003-0251-z
PDEs in connection with fluid mechanics (35Q35) Stefan problems, phase changes, etc. (80A22) Flows in porous media; filtration; seepage (76S05) Other free boundary flows; Hele-Shaw flows (76D27)
Related Items
Free boundary problems for tumor growth: a viscosity solutions approach, Regularity of the free boundary for the one phase Hele--Shaw problem, Homogenization of the free boundary velocity, Adaptive finite difference methods for nonlinear elliptic and parabolic partial differential equations with free boundaries, Generalized diffusion of vortex: self-similarity and the Stefan problem, On nonlinear cross-diffusion systems: an optimal transport approach, Hydrodynamical and computational aspects and stability problems for viscoplastic flows, On the global existence for the Muskat problem, A Hele–Shaw Limit with a Variable Upper Bound and Drift, Singular limit of the porous medium equation with a drift, Global well‐posedness for the one‐phase Muskat problem, Lyapunov functions, identities and the Cauchy problem for the Hele-Shaw equation, Global stability of steady states in the classical Stefan problem for general boundary shapes, Tumor boundary instability induced by nutrient consumption and supply, Porous medium equation to Hele-Shaw flow with general initial density, Functional inequalities and strong Lyapunov functionals for free surface flows in fluid dynamics, Local Well-Posedness and Global Stability of the Two-Phase Stefan Problem, Regularity for a special case of two-phase Hele-Shaw flow via parabolic integro-differential equations, Congested aggregation via Newtonian interaction, Nonlinear elliptic-parabolic problems, Long-time behavior of the one-phase Stefan problem in periodic and random media, Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium, Homogenization of a Model Problem on Contact Angle Dynamics, Dynamic stability of equilibrium capillary drops, The Hele-Shaw asymptotics for mechanical models of tumor growth, Motion of sets by curvature and derivative of capacity potential, A Variational Approach to the Hele–Shaw Flow with Injection, Well-posedness for the classical Stefan problem and the zero surface tension limit, Interface dynamics in a two-phase tumor growth model, A variational approach to a quasi-static droplet model, Well-posedness of a needle crystal growth problem with anisotropic surface tension, The zero surface tension limit of two-dimensional interfacial Darcy flow, Quasistatic droplets in randomly perforated domains, Homogenization of one-phase Stefan-type problems in periodic and random media, Asymptotic analysis of a contact Hele-Shaw problem in a thin domain, On melting and freezing for the 2D radial Stefan problem, Long time regularity of solutions of the Hele--Shaw problem, A Free Boundary Problem with Curvature, Some free boundary problems recast as nonlocal parabolic equations, Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems, Some flows in shape optimization, The Stefan problem and concavity, Viscosity solutions for a model of contact line motion, On mean curvature flow with forcing, Convexity and the Hele-Shaw equation, Error estimates on homogenization of free boundary velocities in periodic media, A Hele-Shaw limit without monotonicity, Local smoothing effect and existence for the one-phase Hele–Shaw problem with zero surface tension, Global Stability and Decay for the Classical Stefan Problem, A tumor growth model with autophagy: the reaction-(cross-)diffusion system and its free boundary limit, Homogenization of the Hele-Shaw problem in periodic spatiotemporal media, The one-phase Hele-Shaw problem with singularities, Self-similar solutions for the Muskat equation