Variation of constants formula for functional parabolic partial differential equations
| dc.contributor.author | Carrasco, Alexander | |
| dc.contributor.author | Leiva, Hugo | |
| dc.date.accessioned | 2021-08-17T17:09:27Z | |
| dc.date.available | 2021-08-17T17:09:27Z | |
| dc.date.issued | 2007-10-05 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 20 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14344 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Functional partial parabolic equations | |
| dc.subject | Variation of constants formula | |
| dc.subject | Strongly continuous semigroups | |
| dc.title | Variation of constants formula for functional parabolic partial differential equations | |
| dc.type | Article |