Solution of Convection-Diffusion Problems with the Memory Terms

Abstract

In this paper ¹ an approximation solution of the following convection diffusion problem is discussed

$${\partial _t}b\left( u \right) + div\left( {\bar F\left( {t,x,u} \right) - k\left( {t,x,u} \right)\nabla u} \right) = f\left( {t,x,u,s} \right),s\left( {t,x} \right) = \int\limits_0^t {K\left( {t,z} \right)\psi \left( {u\left( {z,x} \right)} \right)dzin\left( {0,T} \right)} \times \Omega ,$$

(1)

where Ω ⊂ ℝ^N is a bounded domain with a Lipschitz continuous boundary ∂Ω, T < ∞.