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Linear neutral partial differential equations: a semigroup approach

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  • Rainer Nagel
  • Nguyen Thieu Huy

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.

Suggested Citation

  • Rainer Nagel & Nguyen Thieu Huy, 2003. "Linear neutral partial differential equations: a semigroup approach," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:602382
    DOI: 10.1155/S0161171203209157
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