Abstract
This present work deals with the blow up of the coupled Klein-Gordon system with strong damping, distributed delay, and source terms, under suitable conditions.
Highlights
In the present paper, we consider the following system: 8 >>>>>>>>>>
They proved that the solutions of a system of wave equations with degenerate damping, viscoelastic term and strong nonlinear sources acting in both equations at the same time are globally nonexisting provided that the initial data are sufficiently large in a bounded domain of Ω
We have studied the blow up of the coupled Klein-Gordon system with strong damping, distributed delay, and source terms, under suitable conditions which are so important that we find them in many applications of natural sciences
Summary
We consider the following system:. 0ðx, ðxÞ, tÞ, vtðx,−tÞ = k0ðx, tÞ ðx, utðx, 0Þ = u1ðxÞ, x ∈ Ω, ð0, τ2Þ, vðx, 0Þ = v0ðxÞ, vtðx, 0Þ = v1ðxÞ, x ∈ Ω, ð1Þ where U0ðxÞ, ut ð7Þ where the authors showed that there were solutions of (7) with initial energy according to suitable assumptions on g They showed the blow up in a finite time. VÞ, ð11Þ where under some restrictions on positive initial energy for certain conditions on the functions f1 and f2, the authors proved the blows up in finite time of solution. F2ðu, ð12Þ they proved that the solutions of a system of wave equations with degenerate damping, viscoelastic term and strong nonlinear sources acting in both equations at the same time are globally nonexisting provided that the initial data are sufficiently large in a bounded domain of Ω As complement to these works, we are working to prove the blow up result with distributed delay of problem (1), under appropriate assumptions, and we prove these results using the energy method.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
