Hyperboloidal layers for hyperbolic equations on unbounded domains

Hyperboloidal layers for hyperbolic equations on unbounded domains

We show how to solve hyperbolic equations numerically on unbounded domains by means of compactification, thereby avoiding the introduction of an artificial outer boundary. The essential ingredient is a suitable transformation of the time coordinate in combination with compactification. Based on this idea, we present a new layer method, called hyperboloidal layers. Accuracy and efficiency of thi...

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.

Attractors for Modulation Equations on Unbounded Domains { Existence and Comparison {

We are interested in the long{time behavior of nonlinear parabolic PDEs deened on unbounded cylindrical domains. For dissipative systems deened on bounded domains, the long{time behavior can often be described by the dynamics in their nite{dimensional attractors. For systems deened on the innnite line, very little is known at present, since the lack of compactness prevents application of the st...

Boundary Conditions for Hyperbolic Systems of Equations on Curved Domains

Our focus in this paper is on the fundamental system of partial differential equation with boundary conditions (the continuous problem) that all types of numerical methods must respect. First, a constant coefficient hyperbolic system of equations which turns into a variable coefficient system of equations by transforming to a non-cartesian domain is considered. We discuss possible formulations ...

Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains