In this paper we prove the global existence of a strong solution to initial boundary value problem for exponential partial differential equation ∂tu−Δe−Δu+e−Δu−1=0. The was proposed as continuum model epitaxial growth crystal surfaces on vicinal with evaporation and deposition effects [6]. Our investigations reveal that must control size both ‖e−Δu(x,0)‖W2,2(Ω) ‖eΔu(x,0)‖∞,Ω suitably achieve ou...

This article presents a methodology for the synthesis of finite-dimensional nonlinear output feedback controllers for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. Initially, the nonlinear parabolic PDE system is expressed with respect to an appropriate time-invariant spatial coordinate, and a representative (with respect to different initi...

Parameterisation of facial expressions on PDE surface representations of human faces are presented in this work. Taking advantage of the boundary-value approach inherent to Bloor-Wilson PDE method, facial expressions are achieved by manipulating the original boundary curves. Such curves are responsible for generating a surface representation of a human face in its neutral configuration, so that...

This paper presents a reformulation of Krylov Subspace Spectral (KSS) Methods, which use Gaussian quadrature in the spectral domain compute high-order accurate approximate solutions to variable-coefficient time-dependent PDE. This reformulation reveals that KSS methods are actually high-order operator splittings that are defined implicitly, in terms of derivatives of the nodes and weights of Ga...

Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit t...