Blow-up of Solutions of Nonclassical Nonlocal Nonlinear Model Equations

Abstract

For a nonlinear nonlocal operator differential equation of the first order, an abstract Cauchy problem is considered that is a generalization of certain model physical examples. For this problem, the existence of a nonextendable (in time) classical solution is proved. Additionally, finite-time blow-up results are obtained under certain sufficient conditions, and bilateral estimates for the blow-up time are derived. Finally, under certain conditions, the problem is proved to be globally well posed regardless of the value of the initial function.