相关论文: Spline-interpolation solution of 3D Dirichlet prob…
The equations for a self-similar solution of an inviscid incompressible fluid are mapped into an integral equation which hopefully can be solved by iteration. It is argued that the exponent of the similarity are ruled by Kelvin's theorem of…
Let $\Omega\subset\r^n$ be a bounded mean convex domain. If $\alpha<0$, we prove the existence and uniqueness of classical solutions of the Dirichlet problem in $\Omega$ for the $\alpha$-singular minimal surface equation with arbitrary…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
We study a two dimensional collision problem for a rigid solid immersed in a cavity filled with a perfect fluid. We are led to investigate the asymptotic behavior of the Dirichlet energy associated to the solution of a Laplace Neumann…
We investigate the variational structure of discrete Laplace-type equations that are motivated by discrete integrable quad-equations. In particular, we explain why the reality conditions we consider should be all that are reasonable, and we…
Under structural conditions which are almost optimal, we derive a quantitative version of boundary estimate then prove existence of solutions to Dirichlet problem for a class of fully nonlinear elliptic equations on Hermitian manifolds.
In this paper we study the Dirichlet problem for fully nonlinear second-order equations on a riemannian manifold. As in a previous paper we define equations via closed subsets of the 2-jet bundle. Basic existence and uniqueness theorems are…
It is shown that the Rayleigh's dissipation function can be successfully applied in the solution of mechanical problems involving friction non-linear in the velocities. Through the study of surfaces at contact we arrive at a simple integral…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
A new semi-analytical solution to the advection-dispersion-reaction equation for modelling solute transport in layered porous media is derived using the Laplace transform. Our solution approach involves introducing unknown functions…
We solve the Cauchy-Dirichlet problem for the minimal surface system in arbitrary dimension and codimension assuming a condition on the variation of the initial submanifold .
In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\mathbb R}^d$ were introduced by Duchon and have become a…
We study the Dirichlet problem for semilinear equations on general open sets with measure data on the right-hand side and irregular boundary data. For this purpose we develop the classical method of orthogonal projection. We treat in a…
On a bounded three-dimensional smooth domain, we consider the generalized oscillon equation with Dirichlet boundary conditions, with time-dependent damping and time-dependent squared speed of propagation. Under structural assumptions on the…
This work is devoted to studying dynamic interpolation for obstacle avoidance. This is a problem that consists of minimizing a suitable energy functional among a set of admissible curves subject to some interpolation conditions. The given…
We construct new stationary weak solutions of the 3D Euler equation with compact support. The solutions, which are piecewise smooth and discontinuous across a surface, are axisymmetric with swirl. The range of solutions we find is different…
A global analysis is presented of solutions for Laplace's equation on three-dimensional Euclidean space in one of the most general orthogonal asymmetric confocal cyclidic coordinate systems which admit solutions through separation of…
The authors consider the Dirichlet problem for the nonstationary Stokes system in a threedimensional cone. They obtain existence and uniqueness results for solutions in weighted Sobolev spaces and prove a regularity assertion for the…
We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the…
The paper deals with the Dirichlet problem for the nonstationary Stokes system in a three-dimensional cone. The auhors study the asymptotics of the solutions near the vertex of the cone.