Analysis of an integro-differential equation arising from modelling of flows with fading memory through fissured media. (English) Zbl 0836.35061

Summary: An analysis of an integro-differential equation with a convolution term is given. Such equations arise in modelling of flows through 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.


35K20 Initial-boundary value problems for second-order parabolic equations
35A35 Theoretical approximation in context of PDEs
45K05 Integro-partial differential equations