In general, higher order elliptic equations and boundary value problems like the biharmonic equation or the linear clamped plate boundary value problem do not enjoy neither a maximum principle nor a comparison principle or – equivalently – a positivity preserving property. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being written ...

For inpainting with linear partial differential equations (PDEs) such as homogeneous or biharmonic diffusion, sophisticated data optimisation strategies have been found recently. These allow high-quality reconstructions from sparse known data. While they have been explicitly developed with compression in mind, they have not entered actual codecs so far: Storing these optimised data efficiently ...

We develop a simple and efficient FFT-based fast direct solver for the biharmonic equation on a disk. The biharmonic equation is split into a coupled system of harmonic problems. We first use the truncated Fourier series expansion to derive a set of coupled singular ODEs, then we solve those singular equations by second-order finite difference discretizations. Using a radial grid with shifting ...

In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem neither a maximum principle nor a comparison principle or – equivalently – a positivity preserving property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being rea...

In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem neither a maximum principle nor a comparison principle or – equivalently – a positivity preserving property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being rea...

We construct infinitely many real-valued, time-periodic breather solutions of power-type nonlinear wave equations. These are obtained from critical points a dual functional and they weakly localized in space. Our abstract framework allows to find similar existence results for the Klein-Gordon equation or biharmonic

We present a fast direct solver methodology for the Dirichlet biharmonic problem in a rectangle. The solver is applicable in the case of the second order Stephenson scheme [34] as well as in the case of a new fourth order scheme, which is discussed in this paper. It is based on the capacitance matrix method ([10], [8]). The discrete biharmonic operator is decomposed into two components. The fir...

A VLSI algorithm for solving a special block–five– diagonal system of linear algebraic equations will be presented. The algorithm is considered for the VLSI parallel computational model where both the time of the algorithm and the area of its design are components of the complexity estimations. The linear system arises from the finite– difference approximation of the first biharmonic boundary v...

In general, higher order elliptic equations and boundary value problems like the biharmonic equation or the linear clamped plate boundary value problem do not enjoy neither a maximum principle nor a comparison principle or – equivalently – a positivity preserving property. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being written ...