On the regularity of the blow-up set for semilinear heat equations

DOI10.1016/S0294-1449(01)00088-9zbMath1012.35039MaRDI QIDQ697659

Hatem Zaag

Publication date: 17 September 2002

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2002__19_5_505_0

zbMATH Keywords

nondegeneracy condition

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Heat equation (35K05) Initial value problems for second-order parabolic equations (35K15)

Related Items (28)

THE SET OF CONCENTRATION FOR SOME HYPERBOLIC MODELS OF CHEMOTAXIS ⋮ Profile for a Simultaneously Blowing up Solution to a Complex Valued Semilinear Heat Equation ⋮ Singular standing-ring solutions of nonlinear partial differential equations ⋮ A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions ⋮ Blow-up set of type I blowing up solutions for nonlinear parabolic systems ⋮ Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation ⋮ Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters ⋮ Modulation theory for the flat blow-up solutions of nonlinear heat equation ⋮ On the effect of higher order derivatives of initial data on the blow-up set for a semilinear heat equation ⋮ Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile ⋮ Blow-up for a semilinear parabolic equation with large diffusion on \(\mathbb R^N\) ⋮ Continuity of the blow-up profile with respect to initial data and to the blow-up point for a semilinear heat equation ⋮ Existence of the maximal weak solution for a class of singular parabolic equations ⋮ 𝒞^1,αRegularity of the Blow-Up Curve at Non Characteristic Points for the One Dimensional Semilinear Wave Equation ⋮ Blow-up for a semilinear parabolic equation with large diffusion on \(\mathbf R^N\). II. ⋮ Blow-up set for a superlinear heat equation and pointedness of the initial data ⋮ Refined regularity of the blow-up set linked to refined asymptotic behavior for the semilinear heat equation ⋮ Construction of a blow-up solution for the complex Ginzburg-Landau equation in a critical case ⋮ Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation ⋮ Blowup solutions for a nonlinear heat equation involving a critical power nonlinear gradient term ⋮ Nontrivial compact blow-up sets of smaller dimension ⋮ Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation ⋮ Blow-up set for a semilinear heat equation with small diffusion ⋮ Blow-up set for type I blowing up solutions for a semilinear heat equation ⋮ Solution to the semilinear wave equation with a pyramid-shaped blow-up surface ⋮ Strongly anisotropic type II blow up at an isolated point ⋮ Existence, uniqueness and asymptotic behavior of solutions for a singular parabolic equation ⋮ Blowing up solutions for nonlinear parabolic systems with unequal elliptic operators

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