# Global existence of solutions of initial-boundary value problem for nonlocal parabolic equation with nonlocal boundary condition

## TL;DR

This paper investigates the conditions under which solutions to a nonlinear nonlocal parabolic equation with nonlocal boundary conditions exist globally or blow up, depending on variable coefficients over time.

## Contribution

It establishes criteria for global existence and blow-up of solutions for a class of nonlinear nonlocal parabolic equations with nonlocal boundary conditions.

## Key findings

- Conditions for global existence of solutions
- Criteria for solution blow-up
- Dependence on variable coefficients over time

## Abstract

We prove global existence and blow-up of solutions of initial-boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition. Obtained results depend on the behavior of variable coefficients for large values of time.