Analysis of an Integro-differential Equation Arising from Modelling of Flows with Fading Memory Through Fissured Media (Journal of Partial Differential Equations, 1995)
An analysis of an integro-differential equation with a convolution term is given. Such equations arise in modelling of flows th rough fissured media, and these integral terms account for fading memory effects exhibited by the flow. We proposed a convergent semi-discrete approximation of the convolution term with a possibly singular kernel. The approximation scheme leads to the existence/uniqueness result for the problem and has strongly favorable numerical aspects.
Keywords: Integro-partial differential equations; existence and uniqueness of solutions; convolution integrals