arXiv subjects

Claudio Carrasco

Publications and source records attributed to Claudio Carrasco.

2 recordsLinked to original sources

arXiv2026

Evolution families and variation of constants formula for abstract functional differential equations with time-dependent infinite delay

In this paper, we consider a class of first-order abstract retarded functional differential equations in Banach spaces, incorporating a time-dependent infinite delay governed by a regulated function. We establish the existence of mild solutions for the nonlinear equation and show that the family of solution maps for the linear equation forms a well-defined evolution family of bounded linear operators on an appropriate phase space. Furthermore, we leverage this evolution family to prove a variation of constants formula for the inhomogeneous linear problem.

math.CA↗

arXiv2025

Asymptotic behavior of the fundamental solution of space-time fractional equations with a reaction term

In this paper, we consider a space-time fractional partial differential equation with a reactive term. We describe the speed of invasion of its fundamental solution, extending recent results in this topic, which had been proved for the one dimensional spatial setting and some fractional parameters involved in the equation. The key tool to achieve these results in a wide range of cases (any spatial dimension, any time and spatial fractional differential parameters, and any polynomial speed of invasion) is the subordination.

math.AP↗