A reaction–diffusion model for a class of nonlinear parabolic equations with moving boundaries: Existence, uniqueness, exponential decay and simulation

The aim of this paper is to establish the existence, uniqueness and asymptotic behaviour of a strong regular solution for a class of nonlinear equations of reaction–diffusion nonlocal type with moving boundaries:ut-a∫Ωtu(x,t)dxuxx=f(x,t),(x,t)∈Qt,u(α(t),t)=u(β(t),t)=0,t>0,u(x,0)=u0(x),x∈Ω0=]α(0),β(0)[,where QtQt is a bounded non-cylindrical domain defined byQt=(x,t)∈R2:α(t)