Renormalized solutions for degenerate elliptic-parabolic problems with nonlinear dynamical boundary conditions and \(L^1\)-data

DOI10.1016/j.jde.2008.02.022zbMath1145.35407OpenAlexW2100349801MaRDI QIDQ925043

Elsie Sterbin Gottlieb

Publication date: 29 May 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.02.022

zbMATH Keywords

renormalized solutionsHele-Shaw problemdegenerate elliptic-parabolic problemsmultiphase Stefan problemsnon-homogeneous Neumann boundary condition

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Free boundary problems for PDEs (35R35)

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Cites Work

• A degenerate diffusion problem with dynamical boundary conditions
• A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions
• \(L^1\) existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• Quasilinear elliptic-parabolic differential equations
• Étude d'une équation doublement non linéaire
• Existence of bounded solutions for non linear elliptic unilateral problems
• Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems
• Entropy solutions for nonlinear degenerate problems
• On a parabolic system with time derivative in the boundary conditions and related free boundary problems
• Uniqueness for nonlinear degenerate problems
• Stefan problems with nonlinear diffusion and convection
• The mesa-limit of the porous-medium equation and the Hele-Shaw problem
• On mild and weak solutions of elliptic-parabolic problems
• Renormalized solution for Stefan type problems: Existence and uniqueness
• Revising uniqueness for a nonlinear diffusion-convection equation
• Problèmes unilateraux
• Neumann problems for a class of nonlinear degenerate parabolic equations
• Quasilinear parabolic systems with dynamical boundary conditions
• A Nonlinear Diffusion Problem with Localized Large Diffusion
• The Ill-Posed Hele-Shaw Model and The Stefan Problem for Supercooled Water
• Boundary regularity for solutions of degenerate elliptic equations
• A variational inequality approach to Hele-Shaw flow with a moving boundary
• On the existence of weak solutions for quasilinear parabolic initial-boundary value problems
• Comments on the validity of a common category of constitutive equations
• The Treatment of Boundary Singularities in Axially Symmetric Problems Containing Discs
• Existence and uniqueness for a degenerate parabolic equation with 𝐿¹-data
• Renormalised solutions of nonlinear parabolic problems with L¹ data: existence and uniqueness
• Existence of renormalized solutions of degenerate elliptic-parabolic problems
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