Stability properties of Radon measure-valued solutions for a class of nonlinear parabolic equations under Neumann boundary conditions

In this paper, we address the existence, uniqueness, decay estimates, and the large-time behavior of the Radon measure-valued solutions for a class of nonlinear strongly degenerate parabolic equations involving a source term under Neumann boundary conditions with bounded Radon measure as initial data. {document}$ {equation*} {cases} uₜ = Δψ(u)+h(t)f(x, t) \ \ &in \ \ Ω×(0, T), \\ ∂ψ(u)/∂η = g(u) \ \ &on \ \ ∂Ω×(0, T), \\ u(x, 0) = u₀(x) \ \ &in \ \ Ω, {cases} {equation*} document where T > 0 $, $ Ω⊂ RN(N≥2) $ is an open bounded domain with smooth boundary $ ∂Ω $, $ η $ is an outward normal vector on $ ∂Ω $. The initial value data $ u₀ $ is a nonnegative bounded Radon measure on $ Ω $, the function $ f $ is a solution of the linear inhomogeneous heat equation under Neumann boundary conditions with measure data, and the functions $ ψ $, $ g $ and $ h $ satisfy the suitable assumptions.