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A semidiscrete scheme for evolution equations with memory

  • * Corresponding author: Filippo Dell'Oro

    * Corresponding author: Filippo Dell'Oro 
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  • 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_t u(t) - \int_0^\infty g(s) \Delta u(t-s)\, {{\rm{d}}} s = 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.

    Mathematics Subject Classification: Primary: 65J08, 45K05; Secondary: 65M12, 45M10.

    Citation:

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