Characteristic surface data for the eikonal equation
نویسندگان
چکیده
منابع مشابه
Characteristic Surface Data for the Eikonal Equation
A method of solving the eikonal equation, in either flat or curved space-times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe the wave-front si...
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 کاملTraveltime computation with the linearized eikonal equation
Traveltime computation is an important part of seismic imaging algorithms. Conventional implementations of Kirchhoff migration require precomputing traveltime tables or include traveltime calculation in the innermost computational loop . The cost of traveltime computations is especially noticeable in the case of 3-D prestack imaging where the input data size increases the level of nesting in co...
متن کاملStripe Patterns and the Eikonal Equation
We study a new formulation for the eikonal equation |∇u| = 1 on a bounded subset of R. Considering a field P of orthogonal projections onto 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 if the domain is a tubular n...
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: Journal of Mathematical Physics
سال: 1999
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.532708