Global behavior of the solutions to nonlinear wave equations with combined power-type nonlinearities with variable coefficients

DOI10.1016/j.na.2024.113504arXiv2310.18775OpenAlexW4391708198WikidataQ128179850 ScholiaQ128179850MaRDI QIDQ6154891

Natalia T. Kolkovska, Nickolai Kutev, Milena Dimova

Publication date: 12 March 2024

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2310.18775

zbMATH Keywords

nonlinear wave equationexistence and uniquenessglobal solutionspotential well methodfinite time blow-upnonlinearities with variable coefficients

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Blow-up in context of PDEs (35B44) Second-order semilinear hyperbolic equations (35L71)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Blowup of a positive-energy solution of model wave equations in nonlinear dynamics
• Global behavior of the solutions to nonlinear Klein-Gordon equation with critical initial energy
• Saddle points and instability of nonlinear hyperbolic equations
• The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Non-existence of global solutions to nonlinear wave equations with positive initial energy
• Nonlinear wave equation with both strongly and weakly damped terms: supercritical initial energy finite time blow up
• A characterization of global and nonglobal solutions of nonlinear wave and Kirchhoff equations
• The dynamics of a nonlinear wave equation
• Global well-posedness of solutions for fourth order dispersive wave equation with nonlinear weak damping, linear strong damping and logarithmic nonlinearity
• Global well-posedness for a class of semilinear hyperbolic equations with singular potentials on manifolds with conical singularities
• Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation
• Hyperbolic and parabolic equations with several opposite-sign source at critical initial energy level in heat and vibrating systems
• Global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity
• Nonexistence of global solutions of abstract wave equations with high energies
• On potential wells and applications to semilinear hyperbolic equations and parabolic equations
• Global solutions and finite time blow up for damped semilinear wave equations
• On global solution of nonlinear hyperbolic equations
• Blow-up theorems for nonlinear wave equations
• Wave equations and reaction-diffusion equations with several nonlinear source terms of different sign
• NONLINEAR WAVE EQUATIONS AND REACTION–DIFFUSION EQUATIONS WITH SEVERAL NONLINEAR SOURCE TERMS OF DIFFERENT SIGNS AT HIGH ENERGY LEVEL
• Blow up and asymptotic behavior in a nondissipative nonlinear wave equation
• Initial boundary value problem for semilinear hyperbolic equations and parabolic equations with critical initial data
• REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS
• A Note on a Nonexistence Theorem for Nonlinear Wave Equations
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Further Global Nonexistence Theorems for Abstract Nonlinear Wave Equations
• Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations