Blow-up results and localization of blow-up points in an \(N\)-dimensional smooth domain

DOI10.1215/S0012-7094-97-08816-5zbMath0884.35071OpenAlexW2081407931MaRDI QIDQ1362086

D. F. Rial, Julio D. Rossi

Publication date: 2 April 1998

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-97-08816-5

zbMATH Keywords

heat equationpositive solutionsnonlinear boundary conditionestimate for the blow-up timeblow-up at the boundary

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (19)

COMPLETE BLOW-UP AND THERMAL AVALANCHE FOR HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS ⋮ Blow-up problems for the heat equation with a local nonlinear Neumann boundary condition ⋮ Parabolic problems with dynamical boundary conditions: eigenvalue expansions and blow up ⋮ Boundary fluxes for nonlocal diffusion ⋮ A convex-concave problem with a nonlinear boundary condition. ⋮ Lifespan estimates via Neumann heat kernel ⋮ The blow-up profile for a nonlocal nonlinear parabolic equation with a nonlocal boundary condition ⋮ Improvements on lower bounds for the blow-up time under local nonlinear Neumann conditions ⋮ Simultaneous versus nonsimultaneous blowup for a system of heat equations coupled boundary flux ⋮ The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation ⋮ Blow-up rate for the heat equation with a memory boundary condition ⋮ Blow-up and convergence results for a one-dimensional non-local parabolic problem ⋮ On numerical blow-up sets ⋮ Global blow-up for a localized nonlinear parabolic equation with a nonlocal boundary condition ⋮ NUMERICAL BLOW-UP TIME FOR A PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITIONS* ⋮ The Porous Medium Equation With Blowing Up Boundary Data ⋮ Global solvability for the heat equation with boundary flux governed by nonlinear memory ⋮ Localization of blow-up points for a parabolic system with a nonlinear boundary condition ⋮ Global blow-up for a localized quasilinear parabolic system with nonlocal boundary conditions

Cites Work

• Blow up results and localization of blow up points for the heat equation with a nonlinear boundary condition
• Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time
• On Existence and Nonexistence in the Large of Solutions of Parabolic Differential Equations with a Nonlinear Boundary Condition
• Global Existence and Blow-Up Problems for Quasilinear Parabolic Equations with Nonlinear Boundary Conditions
• The Profile Near Blowup Time for Solution of the Heat Equation with a Nonlinear Boundary Condition
• Global Behavior of Positive Solutions to Nonlinear Diffusion Problems with Nonlinear Absorption Through the Boundary

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