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Semigroups and Linear Partial Differential Equations with Delay

✍ Scribed by András Bátkai; Susanna Piazzera

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
145 KB
Volume
264
Category
Article
ISSN
0022-247X

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✦ Synopsis

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.

📜 SIMILAR VOLUMES

Integrated Semigroups and Related Partia
Integrated Semigroups and Related Partial Differential Equations
✍ Valentin Keyantuo 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 256 KB

We investigate the relationship between abstract linear evolution equations of heat, wave, and Schrodinger types in terms of well-posedness in Banach spaces. More precisely, we study our operators as generators of integrated semigroups and integrated cosine functions. As applications, we consider i