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Exponential decay estimates for semilinear wave-type equations with time-dependent time delay (2303.14208v1)
Published 24 Mar 2023 in math.AP
Abstract: In this paper, we analyze a semilinear damped second order evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. The nonlinear term satisfies a local Lipschitz continuity assumption. Under appropriate conditions, we prove well-posedness and exponential stability of our model for small initial data. Our arguments combine a Lyapunov functional approach with some continuity arguments. Moreover, as an application of our abstract results, the damped wave equation with a source term and delay feedback is analyzed.