Exponential Stability for the Coupled Klein–Gordon–Schrödinger Equations with Competing Viscoelastic and Frictional Dissipative Effects

This paper aims to study the model of Klein–Gordon–Schrödinger equations with a memory term and locally distributed damping : $$ {\{ {array}{ll} iψ '+ Δ ψ + iα (|ψ |² +1)ψ =- φ ψ ~ in ~Ω × (0, ∞ ), \\ φ '' - Δ φ + ∫ ₀ᵗ g(t-τ ) div[a(x) ∇ φ (τ )] d τ +b(x)φ '= |ψ |2θχ ω ~ in ~Ω × (0, ∞ ),\\ {array}. } $$ i ψ ′ + Δ ψ + i α ( | ψ | 2 + 1 ) ψ = - ϕ ψ in Ω × ( 0 , ∞ ) , ϕ ′ ′ - Δ ϕ + ∫ 0 t g ( t - τ ) d i v [ a ( x ) ∇ ϕ ( τ ) ] d τ + b ( x ) ϕ ′ = | ψ | 2 θ χ ω in Ω × ( 0 , ∞ ) , where $$Ω $$ Ω