Existence and regularity of local solutions to partial neutral functional differential equations with infinite delay

Abstract

In this paper, we establish results concerning, existence, uniqueness, global continuation, and regularity of integral solutions to some partial neutral functional differential equations with infinite delay. These equations find their origin in the description of heat flow models, viscoelastic and thermoviscoelastic materials, and lossless transmission lines models; see for example [15] and [38].

Keywords

• Infinite delay
• integrated semigroup
• neutral type
• phase space
• regularity.