Linear neutral partial differential equations: a semigroup approach

Rainer Nagel and Nguyen Thieu Huy

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-13

Abstract:

We study linear neutral PDEs of the form ( ∂ / ∂ t ) F u t = B F u t + Φ u t , t ≥ 0 ; u 0 ( t ) = φ ( t ) , t ≤ 0 , where the function u ( ⋅ ) takes values in a Banach space X . Under appropriate conditions on the difference operator F and the delay operator Φ , we construct a C 0 -semigroup on C 0 ( ℝ − , X ) yielding the solutions of the equation.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:602382

DOI: 10.1155/S0161171203209157

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