Non-global solutions for a class of fourth-order wave equations

DOI10.32513/TBILISI/1546570883zbMath1435.35258OpenAlexW2940281572MaRDI QIDQ2299520

Tarek Saanouni

Publication date: 21 February 2020

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

Full work available at URL: https://projecteuclid.org/euclid.tbilisi/1546570883

zbMATH Keywords

concavity methodpositive energy

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Initial value problems for higher-order hyperbolic equations (35L30) Blow-up in context of PDEs (35B44) Higher-order semilinear hyperbolic equations (35L76)

Cites Work

• A blowing up wave equation with exponential type nonlinearity and arbitrary positive energy
• Fourth-order damped wave equation with exponential growth nonlinearity
• Stability and instability of fourth-order solitary waves
• Time decay for the nonlinear beam equation
• Finite time blowup for nonlinear Klein-Gordon equations with arbitrarily positive initial energy
• Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
• Global well-posedness of some high-order semilinear wave and Schrödinger type equations with exponential nonlinearity
• Scattering and the Levandosky-Strauss conjecture for fourth-order nonlinear wave equations
• A sufficient condition for finite time blow up of the nonlinear Klein-Gordon equations with arbitrarily positive initial energy
• A Weakly Nonlinear Analysis of Elasto-plastic-Microstructure Models
• Trudinger type inequalities in $\mathbf {R}^N$ and their best exponents
• Spatial patterns. Higher order models in physics and mechanics

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