General Decay and Blowing‐Up Solutions of a Nonlinear Wave Equation With Nonlocal in Time Damping and Infinite Memory
Mokhtar Kirane, Radhouane Aounallah, Lotfi Jlali
Abstract
ABSTRACT This paper shows that long‐term stability and blowing‐up solutions for a nonlinear wave equation with a nonlocal damping of Choi and MacCamy type and a nonlocal dispersion can occur. The method of proof of general decay relies on a suitable Lyapunov functional. The method of proof of blow up in finite time of some solutions relies on the concavity method.
Topics & Concepts
MathematicsBlowing upWave equationNonlinear systemMathematical analysisPhysicsQuantum mechanicsAdvanced Mathematical Physics ProblemsStability and Controllability of Differential EquationsNumerical methods for differential equations