In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of R with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a...

We study the relative value iteration for the ergodic control problem under a nearmonotone running cost structure for a nondegenerate diffusion controlled through its drift. This algorithm takes the form of a quasi-linear parabolic Cauchy initial value problem in Rd. We show that this Cauchy problem stabilizes or, in other words, that the solution of the quasi-linear parabolic equation converge...

We consider a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of the degenerate type. We derive some new L1-gradient type estimates for its solutions which are uniform in the sense that they do not depend on the coefficients nor on the size of the spatial domain. We also give some applications of such estimates to gas dynamics, fi...

This paper establishes an anticipating stochastic differential equation of parabolic type for the expectation of the solution of a stochastic differential equation conditioned on complete knowledge of the path of one of its components. Conversely, it is shown that any appropriately regular solution of this stochastic p.d.e. must be given by the conditional expectation. These results generalize ...

We study the relative value iteration for the ergodic control problem under a nearmonotone running cost structure for a nondegenerate diffusion controlled through its drift. This algorithm takes the form of a quasilinear parabolic Cauchy initial value problem in R. We show that this Cauchy problem stabilizes, or in other words, that the solution of the quasilinear parabolic equation converges f...

A modification of the parabolic Allen–Cahn equation, determined by the substitution of Fick’s diffusion law with a relaxation relation of Cattaneo-Maxwell type, is considered. The analysis concentrates on traveling fronts connecting the two stable states of the model, investigating both the aspects of existence and stability. The main contribution is the proof of the nonlinear stability of the ...

A singularly perturbed linear convection-diffusion problem for heat transfer in two dimensions with a parabolic boundary layer is solved numerically. The numerical method consists of a special piecewise uniform mesh condensing in a neighbourhood of the parabolic layer and a standard finite difference operator satisfying a discrete maximum principle. The numerical computations demonstrate numeri...

In this paper, the collocation method proposed by Cai and Wang1 has been reviewed in detail to solve singularly perturbed reaction diffusion equation of elliptic and parabolic types. The method is based on an interpolating wavelet transform using cubic spline on dyadic points. Adaptive feature is performed automatically by thresholding the wavelet coefficients. Numerical examples are presented ...

In this article, we study a free boundary problem modeling the growth of tumors with drug application. The model consists of two nonlinear second-order parabolic equations describing the diffusion of nutrient and drug concentration, and three nonlinear first-order hyperbolic equations describing the evolution of proliferative cells, quiescent cells and dead cells. We deal with the radially symm...

We consider a competition-diffusion system for two competing species; the density of the first species satisfies a parabolic equation together with a inhomogeneous Dirichlet boundary condition whereas the second one either satisfies a parabolic equation with a homogeneous Neumann boundary condition, or an ordinary differential equation. Under the situation where the two species spatially segreg...