Apr 9, 2014 · We study decay properties of the numerical solutions of a class of partial differential equations $$\begin{aligned} \ddot{u}(t)+Au(t)-\int ...

Decay properties in energy norm for solutions of a class of partial differential equations with memory are studied by means of frequency domain methods.

The proposed discretization uses convolution quadrature based on the trapezoidal rule in time, and piecewise linear finite elements in space to establish ...

Prüss, J.: Decay properties for the solutions of a partial differential equation with memory. Arch. Math. 92, 158–173 (2009)

Let A be an unbounded, self-adjoint, positive definite linear operator on a Hilbert space H and let β ∈ L1(R+) be a scalar memory kernel.

We study decay properties of the numerical solutions of a class of partial differential equations $$\begin{aligned} \ddot{u}(t)+Au(t)-\int \limits ...

Decay Properties for the Numerical Solutions of a Partial Differential Equation with Memory. Da Xu. https://doi.org/10.1007/s10915-014-9850-0. 2014, Journal of ...

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In this paper we consider a linear damping wave equation with a memory effect using exponential kernels. We establish a bound for an energy function that is ...

They showed that the energy decays as fast as the solution of an associated differential equation whose coefficients depend on the damping term. Following ...