The fast diffusion equation with measure data

DOI10.1007/s00030-011-0131-4zbMath1255.35145OpenAlexW1991727506WikidataQ110125280 ScholiaQ110125280MaRDI QIDQ442560

Teemu Lukkari

Publication date: 1 August 2012

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-011-0131-4

zbMATH Keywords

fast diffusion equationweak solutiona priori estimatemeasure datasupercritical rangecompacteness

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) PDEs with measure (35R06)

Related Items (6)

Degenerate and Singular Porous Medium Type Equations with Measure Data ⋮ Solutions with moving singularities for equations of porous medium type ⋮ Sharp boundedness and continuity results for the singular porous medium equation ⋮ Global existence for reaction-diffusion systems with nonlinear diffusion and control of mass ⋮ Existence of weak solutions of doubly nonlinear parabolic equations ⋮ Existence of a renormalized solution to an anisotropic parabolic problem for an equation with diffuse measure

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The porous medium equation with measure data
• Nonlinear parabolic equations involving measures as initial conditions
• Doubly nonlinear evolution equations governed by time-dependent subdifferentials in reflexive Banach spaces
• Degenerate diffusions. Initial value problems and local regularity theory
• Nonlinear elliptic and parabolic equations involving measure data
• Non-negative solutions to fast diffusions
• Asymptotics of the fast diffusion equation via entropy estimates
• Obstacle problem for nonlinear parabolic equations
• Compact sets in the space \(L^ p(0,T;B)\)
• Quasilinear elliptic-parabolic differential equations
• Nonlinear parabolic equations with measure data
• Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities
• On the uniqueness problem for quasilinear elliptic equations involving measures
• Removable sets for continuous solutions of quasilinear elliptic equations
• Degenerate problems with irregular obstacles
• Existence and uniqueness of “entropy” solutions of parabolic problems with L1 data
• Non-negative solutions of theo porous medium eqation
• Definition and properties of supersolutions to the porous medium equation
• The Cauchy Problem for u t = Δu m When 0 < m < 1
• Uniqueness of the solutions of ut−Δϕ(u) = 0 with initial datum a measure
• Renormalised solutions of nonlinear parabolic problems with L¹ data: existence and uniqueness

This page was built for publication: The fast diffusion equation with measure data