Partial Differential Equations in Applied Mathematics (Dec 2024)

Blow-up study of a nonlinear hyperbolic system with delay

  • Mohammad Kafini,
  • Mohammad M. Al-Gharabli,
  • Adel M. Al-Mahdi

Journal volume & issue
Vol. 12
p. 100984

Abstract

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This work examines a system of wave equations that feature frictional damping and nonlinear sources. The two equations are affected by constant delay. By demonstrating that there exist solutions with negative initial energy that blow up in a finite amount of time, we prove a blow-up result. Levine’s concavity approach is a basis of the proof. Additionally, by estimating the lower bound, we dominate the blow-up time from below.

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