Blow-up of Positive Initial Energy Solutions for A System of Nonlinear Wave Equations with Supercritical Sources

2014 ◽  
Vol 20 (2) ◽  
pp. 207-227 ◽  
Author(s):  
Shun-Tang Wu
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Blow Up ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Positive Initial Energy

scholarly journals Blow-Up of Certain Solutions to Nonlinear Wave Equations in the Kirchhoff-Type Equation with Variable Exponents and Positive Initial Energy

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Loay Alkhalifa ◽  
Hanni Dridi ◽  
Khaled Zennir
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Blow Up ◽  
Type Equation ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Variable Exponents ◽  
Quasilinear Wave Equation ◽  
Positive Initial Energy

This paper is concerned with the blow-up of certain solutions with positive initial energy to the following quasilinear wave equation: u t t − M N u t Δ p · u + g u t = f u . This work generalizes the blow-up result of solutions with negative initial energy.

scholarly journals Blow up of solutions for 3D quasi-linear wave equations with positive initial energy

2017 ◽  
Vol 33 (1) ◽  
pp. 97-106
Author(s):  
AMIR PEYRAVI ◽  
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Blow Up ◽  
Nonlinear Damping ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Linear Wave ◽  
Positive Initial Energy ◽  
Nonlinear Anal ◽  
Klein Gordon

In this paper we investigate blow up property of solutions for a system of nonlinear wave equations with nonlinear dissipations and positive initial energy in a bounded domain in R3. Our result improves and extends earlier results in the literature such as the ones in [Zhou, J. and Mu, C., The lifespan for 3D quasilinear wave equations with nonlinear damping terms, Nonlinear Anal., 74 (2011), 5455–5466] and [Pis¸kin, E., Uniform decay and blow-up of solutions for coupled nonlinear Klein-Gordon equations with nonlinear damping terms, Math. Meth. Appl. Scie., 37 (2014), No. 18, 3036–3047] in which the nonexistence results obtained only for negative initial energy or the one in [Ye, Y., Global existence and nonexistence of solutions for coupled nonlinear wave equations with damping and source terms, Bull. Korean Math. Soc., 51 (2014), No. 6, 1697–1710] where blow up results have been not addressed. Estimate for the lower bound of the blow up time is also given.

scholarly journals Global Nonexistence of Positive Initial-Energy Solutions for Coupled Nonlinear Wave Equations with Damping and Source Terms

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Liang Fei ◽  
Gao Hongjun
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Damping ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Source Terms ◽  
Nonexistence Theorem ◽  
Positive Initial Energy ◽  
Global Nonexistence ◽  
Damping And Source Terms

This work is concerned with a system of nonlinear wave equations with nonlinear damping and source terms acting on both equations. We prove a global nonexistence theorem for certain solutions with positive initial energy.

scholarly journals Growth of Solutions with Positive Initial Energy to Systems of Nonlinear Wave Equations with Damping and Source Terms

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Erhan Pişkin
Keyword(s):  
Initial Data ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Initial Boundary ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Source Terms ◽  
Positive Initial Energy ◽  
Damping And Source Terms ◽  
Growth Of Solutions

We consider initial-boundary conditions for coupled nonlinear wave equations with damping and source terms. We prove that the solutions of the problem are unbounded when the initial data are large enough in some sense.

scholarly journals Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Salim A. Messaoudi ◽  
Ala A. Talahmeh
Keyword(s):  
Nonlinear Wave ◽  
Variable Exponent ◽  
Wave Equations ◽  
Blow Up ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Well Posedness

<p style='text-indent:20px;'>This work is concerned with a system of wave equations with variable-exponent nonlinearities acting in both equations. We, first, discuss the well-posedness then prove a blow up result for solutions with negative initial energy.</p>

scholarly journals Existence, Asymptotic Behaviour, and Blow up of Solutions for a Class of Nonlinear Wave Equations with Dissipative and Dispersive Terms

2009 ◽  
Vol 64 (5-6) ◽  
pp. 315-326
Author(s):  
Necat Polat ◽  
Doğan Kaya
Keyword(s):  
Asymptotic Behaviour ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Term ◽  
Blow Up ◽  
Suitable Condition ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Energy ◽  
Nonlinear Wave Equations

Abstract We consider the existence, both locally and globally in time, the asymptotic behaviour, and the blow up of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative and dispersive terms. Under rather mild conditions on the nonlinear term and the initial data we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the solution decays exponentially to zero as t →+∞. Finally, under a suitable condition on the nonlinear term, we prove that the local solutions with negative and nonnegative initial energy blow up in finite time.

scholarly journals Nonexistence of global solutions for damped abstract wave equations with memory

2021 ◽  
Vol 2090 (1) ◽  
pp. 012117
Author(s):  
Jorge A. Esquivel-Avila
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Initial Energy ◽  
Nonlinear Wave Equations ◽  
Positive Initial Energy ◽  
Viscoelastic Wave ◽  
With Memory

Abstract We consider a class of abstract nonlinear wave equations with memory and linear dissipation. We give sufficient conditions in terms of the nitial data to prove the nonexistence of global solutions. We improve recent results that have studied this problem for viscoelastic wave, Kirchhoff and Petrovsky equations with positive initial energy values.

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