A SEMIDISCRETE SCHEME FOR EVOLUTION EQUATIONS WITH MEMORY

Filippo Dell'Oro , Olivier Goubet (1) , Youcef Mammeri (1) , Vittorino Pata

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We introduce a new mathematical framework for the time discretization of evolution equations with memory. As a model, we focus on an abstract version of the equation partial derivative(t)u(t) - integral(infinity)(0) g(s)Delta u(t - s) ds = 0 with Dirichlet boundary conditions, modeling hereditary heat conduction with Gurtin-Pipkin thermal law. Well-posedness and exponential stability of the discrete scheme are shown, as well as the convergence to the solutions of the continuous problem when the time-step parameter vanishes.

Domaines: Mathématiques [math]

Filippo Dell'Oro, Olivier Goubet, Youcef Mammeri, Vittorino Pata. A SEMIDISCRETE SCHEME FOR EVOLUTION EQUATIONS WITH MEMORY. Discrete and Continuous Dynamical Systems - Series A, 2019, 39 (10), pp.5637-5658. ⟨10.3934/dcds.2019247⟩. ⟨hal-03621775⟩