Some existence and regularity results for porous media and fast diffusion equations with a gradient term

DOI10.1090/S0002-9947-2015-06125-XzbMath1316.35147arXiv1210.5062OpenAlexW1985762192MaRDI QIDQ5247018

Boumediene Abdellaoui, Magdalena Walias, Ireneo Peral Alonso

Publication date: 22 April 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.5062

zbMATH Keywords

fast diffusion equationporous media equationgradient dependenceelliptic-parabolic equations

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Second-order parabolic equations (35K10) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Singular parabolic equations (35K67) Quasilinear parabolic equations (35K59)

Related Items (4)

Existence to nonlinear parabolic problems with unbounded weights ⋮ Reaction-diffusion systems with initial data of low regularity ⋮ On the KPZ equation with fractional diffusion: global regularity and existence results ⋮ A quasilinear singular elliptic problem related to the Kardar–Parisi–Zhang equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The porous medium equation with measure data
• Elliptic problems with nonlinear terms depending on the gradient and singular on the boundary
• Approximated solutions of equations with \(L^ 1\) data. Application to the \(H\)-convergence of quasilinear parabolic equations
• Quasilinear elliptic-parabolic differential equations
• Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems
• Entropy solutions for nonlinear degenerate problems
• Nonlinear parabolic equations with measure data
• Stefan problems with nonlinear diffusion and convection
• \(L^ 1\)-contraction and uniqueness for quasilinear elliptic-parabolic equations
• On parabolic initial-boundary value problems with critical growth for the gradient
• On mild and weak solutions of elliptic-parabolic problems
• Existence results for a class of porous medium type equations with a quadratic gradient term
• Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term
• Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient terms
• Existence results for some quasilinear parabolic equations
• Definition and properties of supersolutions to the porous medium equation
• On the existence of weak solutions for quasilinear parabolic initial-boundary value problems
• Existence and uniqueness for a degenerate parabolic equation with 𝐿¹-data
• Sur un problème parabolique-elliptique
• Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation
• Multiplicity results for porous media and fast diffusion equations with a quadratic gradient term

This page was built for publication: Some existence and regularity results for porous media and fast diffusion equations with a gradient term