Variation of constants formula for functional parabolic partial differential equations
Date
2007-10-05
Authors
Carrasco, Alexander
Leiva, Hugo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
This 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.
Description
Keywords
Functional partial parabolic equations, Variation of constants formula, Strongly continuous semigroups
Citation
Carrasco, 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.
Rights
Attribution 4.0 International