Abstract
In this work, the exponential growth of solutions for a coupled nonlinear Klein–Gordon system with distributed delay, strong damping, and source terms is proved. Take into consideration some suitable assumptions.
Highlights
In modeling in the biological, physical, and social sciences, it is sometimes necessary to take account of optimal control or time delays inherent in the phenomena
How does the qualitative behavior depend on the form and magnitude of the delays? In this paper we examine how we can apply the distributed delay term for knowing the behavior of growth of solutions for a coupled nonlinear Klein–Gordon system with strong damping, source terms
In [12], the authors proved the exponential decay of the following problem: t utt – u + g(t – s) u(s) ds + a(x)ut + |u|γ .u = 0
Summary
In modeling in the biological, physical, and social sciences, it is sometimes necessary to take account of optimal control or time delays inherent in the phenomena (see for example [4, 16]). In [12], the authors proved the exponential decay of the following problem: t utt – u + g(t – s) u(s) ds + a(x)ut + |u|γ .u = 0. For problem (1.1) and with μ1 = 0, for example, in [18], the authors proved a blow-up result for the following problem:
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