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

Peszynska, Malgorzata

J. Partial Differ. Equations 8, No. 2, 159-173 (1995).

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.

MSC:

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

Keywords:

convolution term; flows through fissured media; fading memory effects; semi-discrete approximation