Semigroups and Linear Partial Differential Equations with Delay

By Andr'as B'atkai, Susanna Piazzera. 2001

126 citations recorded by the source corpus.

Abstract We prove the equivalence of the well-posedness of a partial differential equation with delay and an associated abstract Cauchy problem. This is used to derive sufficient conditions for well-posedness, exponential stability and norm continuity of the solutions. Applications to a reaction–diffusion equation with delay are given.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/e85e8ae15784990137552d811566d2cf861b2d69

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Rostyslav Hryniv
2. Carlos Lizama
3. András Bátkai
4. Gaston M. N'Guérékata
5. Christopher S. Goodrich
6. Charles T. Fulton
7. Chuang Chen
8. Miao Li

In Computational Theory and Mathematics

1. A. Dijksma
2. Paul Binding
3. Rostyslav Hryniv
4. Carlos Lizama
5. András Bátkai

In Control and Systems Engineering

1. Carlos Lizama
2. András Bátkai
3. Gaston M. N'Guérékata
4. Chuang Chen
5. Miao Li

Citations in the corpus

• Fourier multipliers and periodic solutions of delay equations in Banach spaces (2006, background): “1) and the solutions of the abstract Cauchy problem U ′(t) = AU(t) + F(t) t ≥ 0, where A = ( A F 0 d/dσ ) ; see [5, 19] and references therein.”
• Spectral problems for operator matrices (2005, background): “In comparison with the recent works [5], [6], [22] on matrix operators of the form (1.”