Reaction-diffusion-convection problems in unbounded cylinders.

Existence of reaction-diffusion-convection waves in unbounded strips

Existence of reaction-diffusion-convection waves in unbounded strips is proved in the case of small Rayleigh numbers. In the bistable case the wave is unique, in the monostable case they exist for all speeds greater than the minimal one. The proof uses the implicit function theorem. Its application is based on the Fredholm property, index, and solvability conditions for elliptic problems in unb...

Hybridized Discontinuous Galerkin Method for Convection-Diffusion-Reaction Problems

In this paper, we propose a new hybridized discontinuous Galerkin method for the convection-diffusion-reaction problems with mixed boundary conditions. The coercivity of the convection-reaction part is achieved by adding an upwinding term. We give error estimates of optimal order in the piecewise H1-seminorm. Furthermore, we show that the approximate solution of our scheme is close to that of t...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

Pullback D-attractors for non-autonomous partly dissipative reaction-diffusion equations in unbounded domains

At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.

Equidistribution grids for two-parameter convection–diffusion boundary-value problems

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...