The numerical solution of a parabolic convection diffusion equation with delay term is considered. This includes both variants, the initial value problem and the prehistory problem. Equations with a delay or memory term, often called integrodifferential problems, appear in different contexts of heat conduction in materials with memory, viscoelasticity and population models. This work concentrat...

We show that the combination of several numerical techniques, including multiscale preconditionning and Richardson extrapolation, yields stable and accurate explicit schemes with large time steps for parabolic evolution equations. Our theoretical study is limited here to linear problems (typically the Heat equation with non-constant coee-cients). However, the extrapolation procedures that we st...

AbslraclRigorous bounds on temperature and concentration are obtained for a model reacting system incorporating spatial variation, reactant consumption, and Arrhenius kinetics. Similar bounds are obtained for the Semenov (spatially uniform) approximation. Temperatures predicted by the FrankKamenetskii (stationaryl approximation are shown to be upper bounds on the temperature of the complete tim...

We give sufficient conditions to have the finite extinction for all solutions of linear parabolic reaction-diffusion equations of the type ∂u ∂t − ∆u = −M(t)u(t − τ , x) (1) with a delay term τ > 0, on Ω, an open set of R N , M(t) is a bounded linear map on L p (Ω), u(t, x) satisfies a homogeneous Neumann or Dirichlet boundary condition. We apply this result to obtain distributed null controlla...

A Gauss–Galerkin finite-difference method is proposed for the numerical solution of a class of linear, singular parabolic partial differential equations in two space dimensions. The method generalizes a Gauss– Galerkin method previously used for treating similar singular parabolic partial differential equations in one space dimension. Two test problems are studied and the numerical results are ...

It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells. Additionally, many semilinear parabolic equations have equilibria with finite dimensional unstable manifolds. In this article, these results are unified to show that for a specific parabolic equation on an unbounded domain, the space of hete...

We prove that the approximate null-controllability with uniform cost of hypoelliptic Ornstein–Uhlenbeck equations posed on is characterized by an integral thickness geometric condition control supports. also provide associated quantitative weak observability estimates. This result for deduced from same study a large class nonautonomous elliptic moving generalize in particular results known para...