Well-Posedness and General Decay of Solutions for the Heat Equation with a Time Varying Delay Term

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DOI: 10.46793/KgJMat2202.267B


We consider the nonlinear heat equation in a bounded domain with a time varying delay term

ut + Δ2u  −  J (t)    g (t− s )Δ2u  (s)ds + αK   (t)u + βK  (t)u (t −  τ(t)) =  0,
with initial conditions. By introducing suitable energy and Lyapunov functionals, under some assumptions, we then prove a general decay result of the energy associated of this system under some conditions.


Heat equation, time varying delay, energy decay, Lyapunov functional, global existence, viscoelastic term.


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