Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation

DOI10.1215/S0012-7094-06-13333-1zbMath1096.35062MaRDI QIDQ2497194

Hatem Zaag

Publication date: 3 August 2006

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

Full work available at URL: https://projecteuclid.org/euclid.dmj/1150201200

zbMATH Keywords

refined regularity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Analyticity in context of PDEs (35A20) Initial value problems for second-order parabolic equations (35K15)

Related Items (21)

Excluding blowup at zero points of the potential by means of Liouville-type theorems ⋮ Singular standing-ring solutions of nonlinear partial differential equations ⋮ 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 ⋮ 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 ⋮ 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 ⋮ 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 ⋮ A Simplified Approach to the Refined Blowup Behavior for the Nonlinear Heat Equation ⋮ Refined regularity of the blow-up set linked to refined asymptotic behavior for the semilinear heat equation ⋮ Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation ⋮ Nontrivial compact blow-up sets of smaller dimension ⋮ 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 ⋮ A simplified proof of a Liouville theorem for nonnegative solution of a subcritical semilinear heat equations ⋮ Solution to the semilinear wave equation with a pyramid-shaped blow-up surface ⋮ Strongly anisotropic type II blow up at an isolated point ⋮ Blowing up solutions for nonlinear parabolic systems with unequal elliptic operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the blowup of multidimensional semilinear heat equations
• On the regularity of the blow-up set for semilinear heat equations
• Single point blow-up for a semilinear initial value problem
• Differentiability of the blow-up curve for one dimensional nonlinear wave equations
• Refined uniform estimates at blow-up and applications for nonlinear heat equations
• One dimensional behavior of singular \(n\)-dimensional solutions of semilinear heat equations
• Stability of the blow-up profile of nonlinear heat equations from the dynamical system point of view
• Determination of the blow-up rate for a critical semilinear wave equation
• Blowup for nonlinear hyperbolic equations
• A Liouville theorem for vector-valued nonlinear heat equations and applications
• Blow-up behaviour of one-dimensional semilinear parabolic equations
• Nondegeneracy of blowup for semilinear heat equations
• Asymptotically self‐similar blow‐up of semilinear heat equations
• The Blow-Up Boundary for Nonlinear Wave Equations
• Higher Dimensional Blow Up for Semilinear Parabolic Equations
• Refined asymptotics for the blowup of u_t — δu = u^p
• Classification of Singularities for Blowing up Solutions in Higher Dimensions
• Determination of the blow-up rate for the semilinear wave equation
• Boundedness up to blow-up of the difference between two solutions to a semilinear heat equation
• Blow up rate for semilinear heat equations with subcritical nonlinearity
• Universality in blow-up for nonlinear heat equations

This page was built for publication: Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation