Solution to the semilinear wave equation with a pyramid-shaped blow-up surface

DOI10.5802/SLSEDP.104zbMath1475.35209OpenAlexW2727594163MaRDI QIDQ2053915

Frank Merle, Hatem Zaag

Publication date: 30 November 2021

Published in: Séminaire Laurent Schwartz. EDP et Applications (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=SLSEDP_2016-2017____A6_0/

zbMATH Keywords

semilinear wave equationblow-upcharacteristic pointmulti-solitonshigher dimensional case

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Shocks and singularities for hyperbolic equations (35L67) Wave equation (35L05) Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Soliton solutions (35C08) Second-order semilinear hyperbolic equations (35L71)

Cites Work

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• Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem
• Blow-up results for semilinear wave equations in the superconformal case
• Blow-up behavior for the Klein-Gordon and other perturbed semilinear wave equations
• Construction and stability of a blow up solution for a nonlinear heat equation with a gradient term
• Stable self-similar blow up for energy subcritical wave equations
• Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations
• Blow-up behavior outside the origin for a semilinear wave equation in the radial case
• On pointwise decay of linear waves on a Schwarzschild black hole background
• Stability of the blow-up profile for equations of the type \(u_ t=\Delta u+| u| ^{p-1}u\)
• On the regularity of the blow-up set for semilinear heat equations
• Construction of solutions to the subcritical gKdV equations with a given asymptotical behavior
• Multi solitary waves for nonlinear Schrödinger equations
• Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile
• Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity
• Blow-up profile for the complex Ginzburg-Landau equation
• Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation
• Construction of solutions to the \(L^2\)-critical KdV equation with a given asymptotic behaviour
• Differentiability of the blow-up curve for one dimensional nonlinear wave equations
• Stable blow-up patterns
• Blow-up results for vector-valued nonlinear heat equations with no gradient structure
• One dimensional behavior of singular \(n\)-dimensional solutions of semilinear heat equations
• Determination of the blow-up rate for a critical semilinear wave equation
• Blowup for nonlinear hyperbolic equations
• Stability and asymptotic stability for subcritical gKdV equations
• Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation
• Type II blow-up for the four dimensional energy critical semi linear heat equation
• On the stability of critical chemotactic aggregation
• Classification of the radial solutions of the focusing, energy-critical wave equation
• Blowup behaviour for the nonlinear Klein-Gordon equation
• Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension
• Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations
• Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation
• On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations
• Threshold Behavior for Nonlinear Wave Equations
• Dynamics near the threshold for blowup in the one-dimensional focusing nonlinear Klein-Gordon equation
• Construction of a Multisoliton Blowup Solution to the Semilinear Wave Equation in One Space Dimension
• Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension
• LYAPUNOV FUNCTIONAL AND BLOW-UP RESULTS FOR A CLASS OF PERTURBATIONS OF SEMILINEAR WAVE EQUATIONS IN THE CRITICAL CASE
• A Lyapunov functional and blow-up results for a class of perturbed semilinear wave equations
• Construction of a stable blow-up solution for a class of strongly perturbed semilinear heat equations
• The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions
• Universality of global dynamics for the cubic wave equation
• Profile for a Simultaneously Blowing up Solution to a Complex Valued Semilinear Heat Equation
• Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions
• The Blow-Up Boundary for Nonlinear Wave Equations
• Solution of a nonlinear heat equation with arbitrarily given blow-up points
• Determination of the blow-up rate for the semilinear wave equation
• Existence of a stable blow-up profile for the nonlinear heat equation with a critical power nonlinear gradient term
• On blowup for semilinear wave equations with a focusing nonlinearity
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Universality in blow-up for nonlinear heat equations
• Multi-solitons and Related Solutions for the Water-waves System
• Existence and stability of a blow-up solution with a new prescribed behavior for a heat equation with a critical nonlinear gradient term
• Stable blow up dynamics for energy supercritical wave equations
• Asymptotic N -soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations

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