Nonlinear boundary value problems relative to one dimensional heat equation

DOI10.13137/2464-8728/30914zbMath1459.35258arXiv2006.03335MaRDI QIDQ4963471

Laurent Véron

Publication date: 18 February 2021

Full work available at URL: https://arxiv.org/abs/2006.03335

zbMATH Keywords

singularitiesMarcinkiewicz spacesRadon measuresnonlinear heat flux

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Heat equation (35K05) Self-similar solutions to PDEs (35C06) Second-order semilinear hyperbolic equations (35L71) PDEs with measure (35R06)

Cites Work

• Heat equation with a nonlinear boundary condition and uniformly local \(L^r\) spaces
• Fractional heat equations with subcritical absorption having a measure as initial data
• Global solutions of the heat equation with a nonlinear boundary condition
• Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition
• On the inequality \(\Delta u \geqq f (u)\)
• Nonlinear parabolic equations involving measures as initial conditions
• A very singular solution of the heat equation with absorption
• Semilinear parabolic equations with measure boundary data and isolated singularities
• On solutions of δu=f(u)
• Variational problems related to self-similar solutions of the heat equation
• The blow‐up rate for the heat equation with a non‐linear boundary condition
• Isolated boundary singularities of signed solutions of some semilinear parabolic equations
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