Abstract
In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.
Highlights
In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay
In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations in the form d dt (x(t)
In the classic theory of heat conduction, it is assumed that the internal energy and the heat flux depends linearly on the temperature u(·) and on its gradient ∇u(·)
Summary
In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations in the form d dt (x(t). Abstract partial neutral integro-differential equations with unbounded delay arises, for instance, in the theory development in Gurtin & Pipkin [13] and Nunziato [28] for the description of heat conduction in materials with fading memory. In the classic theory of heat conduction, it is assumed that the internal energy and the heat flux depends linearly on the temperature u(·) and on its gradient ∇u(·) Under these conditions, the classic heat equation describes sufficiently well the evolution of the temperature in different types of materials. To the best of our knowledge, the study of the existence and qualitative properties of solutions of neutral integro-differential equations with unbounded delay described in the abstract form (1.1) are untreated topics in the literature and this, is the main motivation of this article
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
