On global solvability and asymptotic behaviour of a mixed problem for a nonlinear degenerate Kirchhoff model in moving domains

In this paper we prove the existence, uniqueness and asymptotic behaviour of global regular solutions of the mixed problem for the Kirchhoff nonlinear model given by the hyperbolic-parabolic equation (ρ₁uₜ)ₜ + ρ₂uₜ - M(t,∫α(t)β(t) |uₓ|²dx)uₓₓ = f in Q, where Q = \(x,t)∈ R²| α(t) < x < β(t), 0 < t < ∞\ is a noncylindrical domain of R² and β(·), α(·) are positive functions such that limt→∞(β(t) - α(t)) = + ∞. The real function M(·,·) is such that M(t,λ) ≥ m₀ > 0 ∀ (t,λ)∈ [0,∞[×[0,∞[, while ρ₁(·), ρ₂(·) are given functions which satisfy some appropriate conditions.