Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation

DOI10.1215/00127094-1902040zbMath1270.35320arXiv1010.0618OpenAlexW2124296680MaRDI QIDQ1928330

Frank Merle, Hatem Zaag

Publication date: 3 January 2013

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

Full work available at URL: https://arxiv.org/abs/1010.0618

zbMATH Keywords

power nonlinearitycharacteristic pointblow-up curve

Mathematics Subject Classification ID

Blow-up in context of PDEs (35B44) Second-order semilinear hyperbolic equations (35L71)

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Cites Work

• Unnamed Item
• Unnamed Item
• Convergence, asymptotic periodicity, and finite-point blow-up in one- dimensional semilinear heat equations
• Continuity of the blow-up profile with respect to initial data and to the blow-up point for a semilinear heat equation
• On the regularity of the blow-up set for semilinear heat equations
• Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation
• Differentiability of the blow-up curve for one dimensional nonlinear wave 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
• The global Cauchy problem for the critical nonlinear wave equation
• Blowup for nonlinear hyperbolic equations
• On existence and scattering with minimal regularity for semilinear wave equations
• Blow-up behaviour of one-dimensional semilinear parabolic equations
• Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension
• Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation
• Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension
• The Blow-Up Boundary for Nonlinear Wave Equations
• The zero set of a solution of a parabolic equation.
• Blow–Up Profiles in One–Dimensional. Semilinear Parabolic Problems
• Higher Dimensional Blow Up for Semilinear Parabolic Equations
• Classification of Singularities for Blowing up Solutions in Higher Dimensions
• Blow-up Surfaces for Nonlinear Wave Equations, I
• Blow-up surfaces for nonlinear wave equations, II
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Exceptional blowup solutions to quasilinear wave equations

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