Carrasco, AlexanderLeiva, Hugo2021-08-172021-08-172007-10-05Carrasco, A., & Leiva, H. (2007). Variation of constants formula for functional parabolic partial differential equations. <i>Electronic Journal of Differential Equations, 2007</i>(130), pp. 1-20.1072-6691https://hdl.handle.net/10877/14344This paper presents a variation of constants formula for the system of functional parabolic partial differential equations ∂u(t, x)/∂t = DΔu + Lut + ƒ(t, x), t > 0, u ∈ ℝn ∂u(t, x)/∂η = 0, t > 0, x ∈ ∂Ω u(0, x) = φ(x) u(s, x) = φ(s, x), s ∈ [-τ, 0), x ∈ Ω. Here Ω is a bounded domain in ℝn, the n x n matrix D is block diagonal with semi-simple eigenvalues having non negative real part, the operator L is bounded and linear, the delay in time is bounded, and the standard notation ut(x)(s) = u(t + s, x) is used.Text20 pages1 file (.pdf)enAttribution 4.0 InternationalFunctional partial parabolic equationsVariation of constants formulaStrongly continuous semigroupsArticle