Solvability of the Heat Equation with a Nonlinear Boundary Condition

DOI10.1137/17M1131416MaRDI QIDQ4626464

Kotaro Hisa, Kazuhiro Ishige

Publication date: 28 February 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.07992

zbMATH Keywords

heat equationnonlinear boundary conditionblow-up timeinitial trace

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (12)

Nonlinear Neumann boundary value problem for semilinear heat equations with critical power nonlinearities ⋮ Optimal singularities of initial functions for solvability of a semilinear parabolic system ⋮ Heat equation with an exponential nonlinear boundary condition in the half space ⋮ Existence of solutions to nonlinear parabolic equations via majorant integral kernel ⋮ Existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces ⋮ Initial traces and solvability for a semilinear heat equation on a half space of ℝ^{ℕ} ⋮ Quantitative description on initial trace for the solvability to heat equation with exponential boundary in unbounded domain ⋮ Existence of solutions for an inhomogeneous fractional semilinear heat equation ⋮ Existence of solutions for a higher-order semilinear parabolic equation with singular initial data ⋮ Sharp Estimate of the Life Span of Solutions to the Heat Equation with a Nonlinear Boundary Condition ⋮ Initial traces and solvability of Cauchy problem to a semilinear parabolic system ⋮ Solvability of superlinear fractional parabolic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Heat equation with a nonlinear boundary condition and uniformly local \(L^r\) spaces
• Supersolutions for a class of semilinear heat equations
• Initial trace for a doubly nonlinear parabolic equation
• Optimal existence and uniqueness theory for the fractional heat equation
• Global solutions of the heat equation with a nonlinear boundary condition
• The Cauchy problem for the Finsler heat equation
• Non-negative solutions of the evolution p-Laplacian equation. Initial traces and Cauchy problem when \(1<p<2\)
• Critère d'existence de solutions positives pour des équations semi- linéaires non monotones. (Existence condition of positive solutions of non-monotonic semilinear equations)
• Parabolic problems with nonlinear boundary conditions and critical nonlinearities
• Existence of solutions for a fractional semilinear parabolic equation with singular initial data
• Cauchy problem and initial traces for a doubly nonlinear degenerate parabolic equation
• Initial trace of solutions of some quasilinear parabolic equations with absorption
• On the Cauchy problem and initial traces for the evolution \(p\)-Laplacian equations with strongly nonlinear sources
• On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary
• Heat equation with a nonlinear boundary condition and growing initial data.
• Supersolutions for a class of nonlinear parabolic systems
• On the Cauchy Problem and Initial Traces for a Degenerate Parabolic Equation
• The Initial Trace of a Solution of the Porous Medium Equation
• The Cauchy Problem for u t = Δu m When 0 < m < 1
• Global Existence, Large Time Behavior and Life Span of Solutions of a Semilinear Parabolic Cauchy Problem
• Initial trace of positive solutions of some nonlinear parabolic equations
• NON WELL POSEDNESS OF PARABOLIC EQUATIONS WITH SUPERCRITICAL NONLINEARITIES
• Local existence of general nonlinear parabolic systems
• On the Existence of Solutions of the Cauchy Problem for a Doubly Nonlinear Parabolic Equation
• Positive Temperatures on an Infinite Rod

This page was built for publication: Solvability of the Heat Equation with a Nonlinear Boundary Condition