Abstract
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 Qt is a bounded non-cylindrical domain defined byQt=(x,t)∈R2:α(t)<x<β(t),forall0<t<T.Moreover, we study the properties of the solution and implement a numerical algorithm based on the Moving Finite Element Method (MFEM) with polynomial approximations of any degree, to solve this class of problems. Some numerical tests are investigated to evaluate the performance of our Matlab code based on the MFEM and illustrate the exponential decay of the solution.
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