Integral formulations of the geometric eikonal equation
نویسندگان
چکیده
منابع مشابه
On the integral equation formulations of some 2D contact problems
We consider integral equation formulations of contact problems of Kirchhoff (thin) plates, discontinuously supported along arcs or segments. In the classical PDE formulation (biharmonic equation), the plate deflection is assumed as the primary unknown. The boundary conditions along the supported edge are imposed in terms of the plate deflection and its derivatives, and the reaction forces and c...
متن کاملA kinetic eikonal equation
We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit (t, x) → (t/ε, x/ε). We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the classical eikonal equation derived from the heat equation with small diffusivity. We prove well-posedness of the phase problem and convergence towards the viscosity sol...
متن کاملNon-oriented solutions of the eikonal equation
We study a new formulation for the eikonal equation |∇u| = 1 on a bounded subset of R. Instead of a vector field ∇u, we consider a field P of orthogonal projections on 1-dimensional subspaces, with divP ∈ L. We prove existence and uniqueness for solutions of the equation P divP = 0. We give a geometric description, comparable with the classical case, and we prove that such solutions exist only ...
متن کاملMultilayered Media Green’s Functions in Integral Equation Formulations
A compact representation is given of the electricand magnetic-type dyadic Green’s functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the axis normal to the stratification. Furthermore, mixed-potential integral equations are derived within the framework of this transmission-line formalism for arbitrarily shaped, conducting or penetrab...
متن کاملBoundary Integral Equation Formulations for Piezoelectric Solids Containing Thin Shapes
A weakly-singular form of the piezoelectric boundary integral equation (BIE) formulation is introduced in this paper, which eliminates the calculation of any singular integrals in the piezoelectric BIE. The crucial question of whether or not the piezoelectric BIE will degenerate when applied to crack and thin shell-like problems is discussed. It can be shown analytically that the conventional B...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Interfaces and Free Boundaries
سال: 2007
ISSN: 1463-9963
DOI: 10.4171/ifb/164