Variation of Constants Formula for Functional Parabolic Partial Differential Equations
نویسندگان
چکیده
This paper presents a variation of constants formula for the system of functional parabolic partial differential equations ∂u(t, x) ∂t = D∆u+ Lut + f(t, x), t > 0, u ∈ R ∂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 × 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.
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