Global solutions of abstract semilinear parabolic equations with memory terms

Abstract

The main purpose of this paper is to obtain the existence of global solutions to semilinear integro-differential equations in Hilbert spaces for rather general convolution kernels and nonlinear terms with superlinear growth at infinity. The included application to a nonlinear model of heat flow in materials of fading memory type provides motivations for the abstract theory

Existence of solutions for abstract neutral integro-differential equations with unbounded delay

“…In the theory developed in [14], [28], the internal energy and the heat flux are described as functionals of u and u x . The next system, see [8], [10], [11], [25], has been frequently used to describe this phenomenon:…”

Existence Results for Abstract Degenerate Neutral Functional Differential Equations

“…In the theory developed in [14,23], the internal energy and the heat flux are described as functionals of u(·) and u x (·). The following equation (see, for example, [6][7][8]22]), has frequently been used to describe this phenomenon:…”

Existence results for abstract neutral functional differential equations

“…In the theory developed in [14,23], the internal energy and the heat flux are described as functionals of and . The next system (see [7,8,9,22]) has been frequently used to describe this phenomena:…”